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{{Short description|Compact astronomical body}}
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{{Use British English|date=August 2024}}
{{Use dmy dates|date=October 2025}}
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| image1        = Black hole - Messier 87 crop max res.jpg
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| alt1          = A black spot, center, surrounded by a doughnut-shaped orange-yellow ring with the blackness of empty space in the background
| caption1      = An image of the core region of [[Messier 87]], a [[supermassive black hole]], processed from a sparse array of [[radio telescopes]] known as the [[Event Horizon Telescope|EHT]] with colours indicating [[brightness temperature]]<ref name="eht19">{{cite journal |display-authors=1 |last1=The Event Horizon Telescope Collaboration |last2=Akiyama |first2=Kazunori |last3=Alberdi |first3=Antxon |last4=Alef |first4=Walter |last5=Asada |first5=Keiichi |last6=Azulay |first6=Rebecca |last7=Baczko |first7=Anne-Kathrin |last8=Ball |first8=David |last9=Baloković |first9=Mislav |last10=Barrett |first10=John |last11=Bintley |first11=Dan |last12=Blackburn |first12=Lindy |last13=Boland |first13=Wilfred |last14=Bouman |first14=Katherine L. |last15=Bower |first15=Geoffrey C. |date=10 April 2019 |title=First M87 Event Horizon Telescope Results. IV. Imaging the Central Supermassive Black Hole |journal=The Astrophysical Journal Letters |volume=875 |issue=1 |pages=L4 |doi=10.3847/2041-8213/ab0e85 |doi-access=free |arxiv=1906.11241 |bibcode=2019ApJ...875L...4E |issn=2041-8205}}</ref><ref>{{cite web |date=10 April 2019 |title=Astronomers capture first image of a black hole |url=https://new.nsf.gov/news/astronomers-capture-first-image-black-hole#image-caption-credit-block |access-date=28 January 2025 |website=new.nsf.gov |language=en}}</ref>

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| alt2          = A black circle, center, surrounded by three bright white blobs of light and the orange-coloured Milky Way distorted into an ark around it. The background is a starry sky with a second image of the Milky Way, not warped, visible in the top left corner.
| caption2      = Simulated view of a [[Schwarzschild black hole|nonspinning, uncharged black hole]] in front of the [[Large Magellanic Cloud]]. The [[gravitational lensing]] effect produces two enlarged but distorted views of the Cloud. Across the top, the [[Milky Way]] disk appears distorted into an arc.<ref name="riazuelo">{{cite journal |author-link= Alain Riazuelo |first= Alain |last= Riazuelo |title= Seeing relativity—I. Ray tracing in a Schwarzschild metric to explore the maximal analytic extension of the metric and making a proper rendering of the stars |journal= International Journal of Modern Physics D |date= 2019|volume= 28 |issue= 2 |page=1950042 |doi= 10.1142/S0218271819500421 |arxiv= 1511.06025 |bibcode= 2019IJMPD..2850042R |s2cid= 54548877 }}</ref>
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A '''black hole''' is an [[astronomical body]] so [[compact object|compact]] that its gravity prevents anything, including light, from escaping. [[Albert Einstein]]'s theory of [[general relativity]], which describes gravitation as the [[curved spacetime|curvature of spacetime]], predicts that any sufficiently compact [[mass]] will form a black hole.<ref name="NYT-20150608">{{Cite news |last=Overbye |first=Dennis |date=June 8, 2015 |title=Black Hole Hunters |url=https://www.nytimes.com/2015/06/09/science/black-hole-event-horizon-telescope.html |access-date=2026-03-28 |work=[[The New York Times]]|language=en-US |issn=0362-4331|url-status=live |archive-url=https://web.archive.org/web/20150609023631/http://www.nytimes.com/2015/06/09/science/black-hole-event-horizon-telescope.html |archive-date=9 June 2015}}</ref> The [[boundary (topology)|boundary]] of no escape is called the [[event horizon]]. In general relativity, crossing a black hole's event horizon traps an object inside but produces no locally detectable change. General relativity also predicts that every black hole should have a central [[gravitational singularity|singularity]], where the [[curvature of spacetime]] is infinite.

Objects whose [[gravitational field]]s are too strong for light to escape were first considered in the 18th century. In 1916, the first solution of general relativity that would characterise a black hole was found. By the late 1950s, this solution began to be interpreted physically as a region of space from which nothing can escape. Black holes were long considered a mathematical curiosity; it was not until the 1960s that theoretical work showed they were a generic prediction of general relativity. The first widely-accepted black hole was [[Cygnus X-1]], identified by several researchers independently in 1971.

Black holes typically form when [[Supernova|very massive stars collapse]] at the end of their [[Stellar evolution|life cycle]]. After a black hole has formed, it can grow by absorbing mass from its surroundings. Supermassive black holes of millions of [[solar mass]]es may form by absorbing stars and merging with other black holes, or via [[Direct collapse black hole|direct collapse]] of [[gas cloud]]s. There is consensus that [[supermassive black hole]]s exist in the centres of most [[galaxies]].

[[Quantum field theory in curved spacetime]] predicts that event horizons emit [[Hawking radiation]], with its rate of emission being inversely proportional to its mass. This causes the black hole to lose mass very slowly, provided it is not [[accretion (astrophysics)|accreting]] matter. However, even the smallest class of black holes observed, [[stellar black hole]]s, are gaining mass from the [[cosmic microwave background]] faster than they are losing mass via Hawking radiation.

The presence of a black hole can be inferred through its interaction with [[matter]] and [[electromagnetic radiation]] such as visible light. Matter falling toward a black hole can form an [[accretion disk]] of infalling plasma, heated by [[friction]] and emitting light. In extreme cases, this creates a [[quasar]], some of the brightest objects in the universe. Merging black holes can be [[interferometry|detected]] by the [[gravitational wave]]s they emit. If stars are orbiting a black hole, their motions can be used to determine the black hole's mass and location. In this way, astronomers have identified numerous stellar black hole candidates in [[binary star|binary systems]] and established that the radio source known as [[Sagittarius A*]], at the core of the [[Milky Way]] galaxy, contains a supermassive black hole of about 4.3{{nbsp}}million [[solar mass]]es.

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== History ==
{{Main|History of black hole physics}}

The idea of a body so massive that even light could not escape was first proposed in the late 18th century by English astronomer and clergyman [[John Michell]] and independently by French scientist [[Pierre-Simon Laplace]]. Both scholars proposed very large stars in contrast to the modern concept of an extremely dense object.<ref name="origin">{{cite journal |last1=Montgomery |first1=Colin |last2=Orchiston |first2=Wayne |last3=Whittingham |first3=Ian |year=2009 |orig-date=Available online 18 April 2023 |title=Michell, Laplace and the Origin of the Black Hole Concept |url=https://researchonline.jcu.edu.au/9892/1/Microsoft_Word_-_Paper__Black_Hole_Concept_Final_.pdf |journal=[[Journal of Astronomical History and Heritage]] | type=Research article |volume=12 |issue=2 |pages=90–96 |bibcode=2009JAHH...12...90M |doi=10.3724/SP.J.1440-2807.2009.02.01 |s2cid=55890996 |doi-access=free}}</ref>

Michell's idea, in a short part of a letter published in 1784,<ref>{{cite journal |last=Michell |first=J. |author-link1=John Michell |date=1784 |title=On the Means of Discovering the Distance, Magnitude, &C. Of the Fixed Stars, In Consequence of the Diminution of the Velocity of Their Light, In Case Such a Diminution Should Be Found to Take Place in Any of Them, And Such Other Data Should Be Procured from Observations, As Would Be Farther Necessary for That Purpose |journal=[[Philosophical Transactions of the Royal Society]] | volume=74 |pages=35–57 |bibcode=1784RSPT...74...35M |doi=10.1098/rstl.1784.0008|jstor=106576|doi-access=free}}</ref> calculated that a star with the same density but 500 times the radius of the sun would not let any emitted light escape; the surface [[escape velocity]] would exceed the [[speed of light]].<ref name="Throne-1994" />{{rp|122}} Michell correctly hypothesized that such non-radiating bodies might be detectable through their gravitational effects on nearby visible bodies.<ref name="origin" /> In 1796, while speculating on the origin of the Solar System in his book {{lang|fr|Exposition du Système du Monde}}, Laplace made a qualitative suggestion that a star could be invisible if it were sufficiently large. [[Franz Xaver von Zach]] asked Laplace for a mathematical analysis, which Laplace provided and published in von Zach's journal ''{{Interlanguage link|Allgemeine Geographische Ephemeriden|de}}''.<ref name="origin" />

=== General relativity ===
{{See also|History of general relativity}}
{{General relativity sidebar|phenomena}}

In 1905, [[Albert Einstein]] showed that the laws of [[electromagnetism]] are identical for observers travelling at different velocities relative to each other. The laws of [[mechanics]] had already been shown to be invariant in this way. However, the theory of gravitation was yet to be included.<ref name="Weinberg-1972">{{cite book |last=Weinberg |first=Steven |url=https://archive.org/details/gravitationcosmo00stev_0 |title=Gravitation and Cosmology |date=1972 |publisher=John Wiley & Sons |isbn=978-0-471-92567-5 |author-link=Steven Weinberg |url-access=registration}}</ref>{{rp|19}} 

In 1907, Einstein published a paper proposing his [[equivalence principle]], the hypothesis that [[inertial mass]] and [[gravitational mass]] have a common cause. Using the principle, Einstein predicted the [[redshift]] and the [[gravitational lensing|lensing]] effect of gravity on light; his prediction of gravitational lensing was one-half of the value that the full theory of general relativity would predict.<ref name="Weinberg-1972" />{{rp|19}} By 1915, Einstein refined these ideas into his [[general theory of relativity]], which explained how matter affects spacetime, which in turn affects the motion of other matter.<ref>{{Cite journal |last=Einstein |first=Albert |author-link=Albert Einstein |date=1915 |title=Feldgleichungen der Gravitation |trans-title=Field Equations of Gravitation |journal=Preussische Akademie der Wissenschaften, Sitzungsberichte |pages=844–847}}</ref><ref>{{Cite journal |last1=Janssen |first1=Michel |last2=Renn |first2=Jürgen |author-link2=Jürgen Renn |date=2015 |title=Arch and Scaffold: How Einstein Found His Field Equations |journal=[[Physics Today]] | type=Feature article |volume=68 |issue=11 |pages=30–36 |bibcode=2015PhT....68k..30J |doi=10.1063/PT.3.2979 |hdl=11858/00-001M-0000-002A-8ED7-1 |doi-access=free |hdl-access=free}}</ref> This formed the basis for black hole physics.<ref>{{Cite book |last1=Fraknoi |first1=Andrew |author-link1=Andrew Fraknoi |url=https://assets.openstax.org/oscms-prodcms/media/documents/Astronomy2e-WEB.pdf |title=Astronomy 2e |last2=Morrison |first2=David |author-link2=David Morrison (astrophysicist) |last3=Wolff |first3=Sidney C. |author-link3=Sidney C. Wolff |date=2022 |publisher=[[OpenStax]] | isbn=978-1-951693-50-3 |edition=2e |pages=839–846 |chapter=24.5 Black Holes |oclc=1322188620 |display-authors=}}</ref>

=== Singular solutions in general relativity ===
Only a few months after Einstein published the [[Einstein field equations|field equations]] describing general relativity, astrophysicist [[Karl Schwarzschild]] set out to apply the idea to stars. He assumed spherical symmetry with no spin and found a [[Schwarzschild metric|solution]] to Einstein's equations.<ref name="Throne-1994" />{{rp|124}}<ref name="Schwarzschild1916">{{cite journal |last=Schwarzschild |first=K. |author-link1=Karl Schwarzschild |date=1916 |title=Über das Gravitationsfeld eines Massenpunktes nach der Einsteinschen Theorie |trans-title=On the gravitational field of a mass point according to Einstein's theory<!-- via translate.google --> |url=https://archive.org/stream/sitzungsberichte1916deutsch#page/188/mode/2up |journal=Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften |volume=7 |pages=189–196 |bibcode=1916SPAW.......189S |via=Internet Archive}}
* Translation: {{cite arXiv |eprint=physics/9905030 |first1=S. |last1=Antoci |first2=A. |last2=Loinger |title=On the Gravitational Field of a Mass Point According to Einstein's Theory |date=12 May 1999<!-- date submitted --> }} and {{cite journal |last=Schwarzschild |first=K. |author-link1=Karl Schwarzschild |date=1916 |title=Über das Gravitationsfeld einer Kugel aus inkompressibler Flüssigkeit nach der Einsteinschen Theorie |url=https://archive.org/stream/sitzungsberichte1916deutsch#page/424/mode/2up |journal=Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften |volume=18 |pages=424–434 |bibcode=1916skpa.conf..424S}}
* Translation: {{cite arXiv |eprint=physics/9912033 |first1=S. |last1=Antoci |title=On the Gravitational Field of a Sphere of Incompressible Fluid According to Einstein's Theory |year=1999 }}</ref> A few months after Schwarzschild, [[Johannes Droste]], a student of [[Hendrik Lorentz]], independently gave the same solution.<ref>{{cite journal |last=Droste |first=J. |date=1917 |title=The Field of a Single Centre in Einstein's Theory of Gravitation, And the Motion of a Particle in That Field |url=http://www.dwc.knaw.nl/DL/publications/PU00012325.pdf |url-status=live |department=Physics |journal=Proceedings of the Section of Sciences |publisher=[[Koninklijke Akademie van Wetenschappen]] | volume=19 |issue=1 |pages=197–215 |bibcode=1917KNAB...19..197D |archive-url=https://web.archive.org/web/20130518034708/http://www.dwc.knaw.nl/DL/publications/PU00012325.pdf |archive-date=18 May 2013 |access-date=16 September 2012}}</ref><ref>{{cite book |title=Studies in the History of General Relativity |editor1-last=Eisenstaedt |editor1-first=Jean |editor2-last=Kox |editor2-first=A. J. |isbn=978-0-8176-3479-7 |date=1992 |publisher=Birkhäuser |chapter=General Relativity in the Netherlands: 1915–1920 |last=Kox |first=A. J. |chapter-url=https://books.google.com/books?id=vDHCF_3vIhUC&pg=PA41 |page=41 |access-date=23 February 2016 |archive-date=10 August 2016 |archive-url=https://web.archive.org/web/20160810215219/https://books.google.com/books?id=vDHCF_3vIhUC&pg=PA41 |url-status=live }}</ref> At a certain radius from the center of the mass, the Schwarzschild solution became [[singularity (mathematics)|singular]], meaning that some of the terms in the Einstein equations became infinite. The nature of this radius, which later became known as the [[Schwarzschild radius]], was not understood at the time.<ref name="HooftHist">{{cite web |last='t Hooft |first=G. |author-link1=Gerard 't Hooft |date=2009 |title=Introduction to the Theory of Black Holes |url=http://www.phys.uu.nl/~thooft/lectures/blackholes/BH_lecturenotes.pdf |url-status=live |archive-url=https://web.archive.org/web/20090521082736/http://www.phys.uu.nl/~thooft/lectures/blackholes/BH_lecturenotes.pdf |archive-date=21 May 2009 |access-date=24 June 2010 |publisher=Institute for Theoretical Physics / Spinoza Institute |pages=47–48}}</ref>

Many physicists of the early 20th century were sceptical of the existence of black holes. In a 1926 popular science book, [[Arthur Eddington]] critiqued the idea of a star with mass compressed to its Schwarzschild radius as a flaw in the then-poorly-understood theory of general relativity.<ref name="eddington1926">{{cite book |first=Arthur |last=Eddington |author-link=Arthur Eddington |date=1926 |title=The Internal Constitution of the Stars |series=Science |volume=52 |issue=1341 |pages=233–40 |url=https://books.google.com/books?id=RjC9DpnWFbkC&pg=PA6 |publisher=Cambridge University Press |url-status=live |archive-url=https://web.archive.org/web/20160811034409/https://books.google.com/books?id=RjC9DpnWFbkC&lpg=PP1&pg=PA6 |archive-date=11 August 2016 |pmid=17747682 |doi=10.1126/science.52.1341.233|bibcode=1920Sci....52..233E }} {{isbn|978-0-521-33708-3}}</ref><ref name="Throne-1994">{{cite book |last1=Thorne |first1=Kip S. |author-link=Kip Thorne |url=https://archive.org/details/blackholestimewa0000thor |title=Black Holes and Time Warps: Einstein's Outrageous Legacy |last2=Hawking |first2=Stephen |author-link2=Stephen Hawking |date=1994 |publisher=[[W. W. Norton & Company]] | isbn=978-0-393-31276-8 |editor-last=Agrawal |editor-first=Milan |edition=1st |access-date=12 April 2019 |url-access=registration}}</ref>{{rp|134|q=The first conclusion was the Newtonian version of light not escaping; the second was a semi-accurate, relativistic description; and the third was typical Eddingtonian hyperbole{{nbsp}}[...] when a star is as small as the critical circumference, the curvature is strong but not infinite, and space is definitely not wrapped around the star. Eddington may have known this, but his description made a good story, and it captured in a whimsical way the spirit of Schwarzschild's spacetime curvature.}} In 1939, Einstein used his theory of general relativity in an attempt to prove that black holes were impossible.<ref name="Bernstein-2007">{{cite magazine |last=Bernstein |first=Jeremy |author-link=Jeremy Bernstein |date=2007 |title=The Reluctant Father of Black Holes |url=https://www.scientificamerican.com/article/the-reluctant-father-of-black-holes-2007-04/ |url-access=subscription |access-date=3 August 2023 |magazine=[[Scientific American]] | pages=4–11 |language=en |volume=17 |doi=10.1038/scientificamerican0407-4sp}}</ref><ref>{{Cite journal |last=Einstein |first=Albert |author-link=Albert Einstein |date=10 May 1939 |title=On a Stationary System With Spherical Symmetry Consisting of Many Gravitating Masses |journal=[[Annals of Mathematics]] | volume=40 |issue=4 |pages=922–936 |doi=10.2307/1968902 |jstor=1968902 }}</ref> His work relied on increasing pressure or increasing centrifugal force balancing the force of gravity so that the object would not collapse beyond its Schwarzschild radius. He missed the possibility that implosion would drive the system below this critical value.<ref name="Throne-1994" />{{rp|135}}

=== Gravity vs degeneracy pressure ===
By the 1920s, astronomers had classified a number of [[white dwarf stars]] as too cool and dense to be explained by the gradual cooling of ordinary stars. In 1926, [[Ralph Fowler]] showed that these stars are not like [[main-sequence star]]s, where thermal pressure balances gravity. Instead, a type of [[degeneracy pressure|quantum-mechanical pressure]] balances gravity at these temperatures and densities.<ref name="Throne-1994" />{{rp|145}} In 1931, [[Subrahmanyan Chandrasekhar]] studied the new [[state of matter]] that results from this balance, called [[electron-degenerate matter]], discovering that it is stable below a certain [[Chandrasekhar limit|limiting mass]]. By 1934 he showed that this explained the catalogue of white dwarf stars.<ref name="Throne-1994" />{{rp|151}} When Chandrasekhar announced his results, Eddington pointed out that stars above this limit would radiate until they were sufficiently dense to prevent light from exiting, a conclusion he considered absurd. Eddington and, later, [[Lev Landau]] argued that some yet unknown mechanism would stop the collapse.<ref>{{cite journal |last=Detweiler |first=S. |author-link=Steven Detweiler |date=1981 |title=Resource Letter BH-1: Black Holes |journal=[[American Journal of Physics]] | type=Paper |volume=49 |issue=5 |pages=394–400 |bibcode=1981AmJPh..49..394D |doi=10.1119/1.12686}}</ref>

In the 1930s, [[Fritz Zwicky]] and [[Walter Baade]] studied [[stellar nova]]e, focusing on exceptionally bright ones they called [[supernova]]e. Zwicky promoted the idea that supernovae produced stars with the density of atomic nuclei—[[neutron stars]]—but this idea was largely ignored at the time.<ref name="Throne-1994" />{{rp|171}} In 1939, based on Chandrasekhar's reasoning, [[J. Robert Oppenheimer]] and [[George Volkoff]] predicted that neutron stars below a certain mass limit, later called the [[Tolman–Oppenheimer–Volkoff limit]], would be stable due to [[neutron degeneracy pressure]]. Above that limit, they reasoned that either their model would not apply or that gravitational contraction would not stop.<ref name="OV1939">{{cite journal |last1=Oppenheimer |first1=J. R. |author-link1=J. Robert Oppenheimer |last2=Volkoff |first2=G. M. |author-link2=George Volkoff |date=1939 |title=On Massive Neutron Cores |journal=[[Physical Review]] | volume=55 |issue=4 |pages=374–381 |doi=10.1103/PhysRev.55.374|bibcode=1939PhRv...55..374O}}</ref>{{rp |page=380 |quote=There would then seem to be only two answers possible to the question of the behaviour of very massive stars: either the equation of state we have used so far fails to describe the behaviour of highly condensed matter that the conclusions reached above are qualitatively misleading, or the star will continue to contract indefinitely, never reaching equilibrium.}}

[[John Archibald Wheeler]] and two of his students resolved questions about the model behind the Tolman–Oppenheimer–Volkoff (TOV) limit. In 1965, Harrison and Wheeler developed the [[equations of state]] relating density to pressure for cold matter all the way through electron degeneracy and neutron degeneracy. Masami Wakano and Wheeler then used the equations to compute the equilibrium curve for stars, relating mass to circumference. They found no additional features that would invalidate the TOV limit. This meant that the only thing that could prevent black holes from forming was a dynamic process ejecting sufficient mass from a star as it cooled.<ref name="Throne-1994" />{{rp|205}}

=== Birth of modern model ===
The modern concept of black holes was formulated by [[Robert Oppenheimer]] and his student [[Hartland Snyder]] in 1939.<ref name="Bernstein-2007" /><ref name="Bartusiak" />{{rp|80}} In the paper,<ref>{{cite journal |last1=Oppenheimer |first1=J.R. |author-link=J. Robert Oppenheimer |last2=Snyder |first2=H. |author-link2=Hartland Snyder |year=1939 |title=On Continued Gravitational Contraction |journal=[[Physical Review]] | type=Highlighted article |volume=56 |issue=5 |pages=455–459 |bibcode=1939PhRv...56..455O |doi=10.1103/PhysRev.56.455 |doi-access=free}}</ref> Oppenheimer and Snyder solved Einstein's equations of general relativity for an idealised imploding star, in a model later called the [[Oppenheimer–Snyder model]], then described the results from far outside the star. The implosion starts as one might expect: the star material rapidly collapses inward. However, as the density of the star increases, [[gravitational time dilation]] increases and the collapse, viewed from afar, seems to slow down further and further until the star reaches its Schwarzschild radius, where it appears frozen in time.<ref name="Throne-1994" />{{rp|217}}

In 1958, [[David Finkelstein]] identified the Schwarzschild surface as an [[event horizon]], calling it "a perfect unidirectional membrane: causal influences can cross it in only one direction". This means that events that occur inside the black hole cannot affect events that occur outside the black hole.<ref>{{cite journal |last=Finkelstein |first=D. |author-link1=David Finkelstein |date=1958 |title=Past-Future Asymmetry of the Gravitational Field of a Point Particle |journal=[[Physical Review]] | type=Article |volume=110 |issue=4 |pages=965–967 |bibcode=1958PhRv..110..965F |doi=10.1103/PhysRev.110.965}}</ref> Finkelstein created a new [[Kruskal–Szekeres coordinates|reference frame]] to include the point of view of infalling observers.<ref name="Bartusiak" />{{rp|103}} Finkelstein's new frame of reference allowed events at the surface of an imploding star to be related to events far away. By 1962 the two points of view were reconciled, convincing many sceptics that implosion into a black hole made physical sense.<ref name="Throne-1994" />{{rp|226}}

=== Golden age ===
[[File:BH-JPL-A&A1979.jpg|alt=A black and white image of a black hole with an accretion disk on punch cards. The black hole is visible as a black semicircle in the center with a white ring overlaid. Around it, a bright white accretion disk wraps around the top and bottom of the black hole and to its sides, appearing brightest on the left side of the black hole.|thumb|The first simulated image of a black hole, created by [[Jean-Pierre Luminet]] in 1978 and featuring the characteristic shadow, [[photon sphere]], and [[gravitational lensing|lensed]] [[accretion disk]]. The disk is brighter on one side due to [[Doppler beaming]].<ref>{{cite journal |last=Luminet |first=J.-P. |date=May 1979 |title=Image of a Spherical Black Hole with Thin Accretion Disk. |url=https://ui.adsabs.harvard.edu/abs/1979A&A....75..228L/abstract |journal=Astronomy and Astrophysics |language=en |volume=75 |pages=228–235 |bibcode=1979A&A....75..228L |issn=0004-6361}}</ref><ref>{{cite web |author=French National Centre for Scientific Research |title=First Ever Image of a Black Hole: A CNRS Researcher Had Simulated It as Early as 1979 |url=https://www.cnrs.fr/en/press/first-ever-image-black-hole-cnrs-researcher-had-simulated-it-early-1979 |website=CNRS |date=10 April 2019 |access-date=18 June 2025}}</ref>]]

The era from the mid-1960s to the mid-1970s was the "golden age of black hole research", when general relativity and black holes became mainstream subjects of research.<ref>{{cite book |last1=Thorne |first1=Kip |author-link=Kip Thorne |url=https://books.google.com/books?id=yLy4b61rfPwC |title=The Future of Theoretical Physics and Cosmology: Celebrating Stephen Hawking's 60th Birthday |publisher=[[Cambridge University Press]] | year=2003 |isbn=0-521-82081-2 |veditors=Shellard ES, [[Gary Gibbons|Gibbons GW]], Rankin SJ |page=74 |chapter=5. Warping spacetime}}</ref><ref name="Throne-1994" />{{rp|p=258}}

In this period, solutions to the equations of general relativity under various different physical constraints were discovered. In 1963, [[Roy Kerr]] found [[Kerr metric|the exact solution]] for a [[rotating black hole]].<ref>{{cite book |last=Kerr |first=R. P. |author-link=Roy Kerr |title=The Kerr Spacetime |date=2009 |publisher=[[Cambridge University Press]] | isbn=978-0-521-88512-6 |editor1-last=Wiltshire |editor1-first=D. L. |chapter=Discovering the Kerr and Kerr-Schild metrics |bibcode=2007arXiv0706.1109K |editor2-last=Visser |editor2-first=M. |editor3-last=Scott |editor3-first=S. M. |arxiv=0706.1109}}</ref> Two years later, [[Ezra T. Newman|Ezra Newman]] found the [[Rotational symmetry#Rotational symmetry with respect to any angle|axisymmetric]] solution for a black hole that is both rotating and [[electrically charged]].<ref>{{cite journal |display-authors=2 |vauthors=[[Ezra T. Newman|Newman ET]], Couch E, Chinnapared K, Exton A, Prakash A, Torrence R |date=1965 |title=Metric of a Rotating, Charged Mass |journal=[[Journal of Mathematical Physics]] | type=Research article |volume=6 |issue=6 |page=918 |bibcode=1965JMP.....6..918N |doi=10.1063/1.1704351}}</ref>

In 1967, [[Werner Israel]] found that the Schwarzschild solution was the only possible solution for a nonspinning, uncharged black hole, meaning that a Schwarzschild black hole would be defined by its [[mass]] alone.<ref>{{cite journal |last=Israel |first=W. |author-link=Werner Israel |date=1967 |title=Event Horizons in Static Vacuum Space-Times |journal=[[Physical Review]] | type=Article |volume=164 |issue=5 |page=1776 |bibcode=1967PhRv..164.1776I |doi=10.1103/PhysRev.164.1776}}</ref> Similar identities were later found for [[Reissner–Nordström metric|Reissner-Nordstrom]] and [[Kerr metric|Kerr]] black holes, defined only by their mass and their charge or spin respectively.<ref>{{cite journal |last=Carter |first=B. |author-link1=Brandon Carter |date=1971 |title=Axisymmetric Black Hole Has Only Two Degrees of Freedom |department=Elementary Particles and Fields |journal=[[Physical Review Letters]] | type=Letter |volume=26 |issue=6 |page=331 |bibcode=1971PhRvL..26..331C |doi=10.1103/PhysRevLett.26.331}}</ref><ref>{{cite book |last=Carter |first=B. |author-link1=Brandon Carter |date=1977 |chapter=The vacuum black hole uniqueness theorem and its conceivable generalisations |title=Proceedings of the 1st Marcel Grossmann Meeting on General Relativity |pages=243–254 }}</ref> Together, these findings became known as the [[no-hair theorem]], which states that a stationary black hole is completely described by the three parameters of the [[Kerr–Newman metric]]: mass, angular momentum, and electric charge.<ref name="HeuslerNoHair" />

At first, it was suspected that the strange mathematical singularities found in each of the black hole solutions only appeared due to the assumption that a black hole would be perfectly [[Rotational symmetry#Rotational symmetry with respect to any angle|spherically symmetric]], and therefore the singularities would not appear in generic situations where black holes would not necessarily be symmetric. This view was held in particular by [[Vladimir A. Belinsky|Vladimir Belinski]], [[Isaak Markovich Khalatnikov|Isaak Khalatnikov]], and [[Evgeny Lifshitz]], who tried to prove that no singularities appear in generic solutions, although they would later reverse their positions.<ref>{{Cite journal |last1=Penrose |first1=Roger |author-link=Roger Penrose |date=1996 |title=Chandrasekhar, Black Holes, And Singularities |journal=[[Journal of Astrophysics and Astronomy]] | type=Article |volume=17 |issue=3–4 |pages=213–231 |bibcode=1996JApA...17..213P |doi=10.1007/BF02702305}}</ref> However, in 1965, [[Roger Penrose]] proved that general relativity predicts that singularities appear in all black holes,<ref name="penrose1965">{{cite journal |last1=Penrose |first1=R. |author-link1=Roger Penrose |date=1965 |title=Gravitational Collapse and Space-Time Singularities |journal=[[Physical Review Letters]] |volume=14 |issue=3 |page=57 |bibcode=1965PhRvL..14...57P |doi=10.1103/PhysRevLett.14.57 |s2cid=116755736}}</ref> although this may not still hold when quantum mechanics is taken into account.<ref>{{cite journal |last1=Ford |first1=L. H. |author1-link=Lawrence Ford |date=2003 |title=The Classical Singularity Theorems and Their Quantum Loopholes |journal=[[International Journal of Theoretical Physics]] | volume=42 |issue=6 |pages=1219–1227 |doi=10.1023/A:1025754515197 |arxiv=gr-qc/0301045 |bibcode=2003gr.qc.....1045F |s2cid=14404560}}</ref>

Astronomical observations also made great strides during this era. In 1967, [[Antony Hewish]] and [[Jocelyn Bell Burnell]] discovered [[pulsar]]s<ref>{{cite journal |display-authors=2 |last1=Hewish |first1=A. |author-link1=Antony Hewish |last2=Bell |first2=S. J. |author-link2=Jocelyn Bell Burnell |last3=Pilkington |first3=J. D. H. |last4=Scott |first4=P. F. |last5=Collins |first5=R. A. |date=1968 |title=Observation of a Rapidly Pulsating Radio Source |journal=[[Nature (journal)|Nature]] | volume=217 |issue=5130 |pages=709–713 |doi=10.1038/217709a0|bibcode=1968Natur.217..709H|s2cid=4277613 }}</ref><ref>{{cite journal |display-authors=2 |last1=Pilkington |first1=J. D. H. |last2=Hewish |first2=A. |author-link2=Antony Hewish |last3=Bell |first3=S. J. |author-link3=Jocelyn Bell Burnell |last4=Cole |first4=T. W. |date=1968 |title=Observations of Some Further Pulsed Radio Sources |journal=[[Nature (journal)|Nature]] | volume=218 |issue=5137 |pages=126–129 |doi=10.1038/218126a0|bibcode=1968Natur.218..126P|s2cid=4253103 }}</ref> and by 1969, these were shown to be rapidly rotating neutron stars.<ref name="araa8_265">{{cite journal |last=Hewish |first=A. |author-link1=Antony Hewish |date=1970 |title=Pulsars |journal=[[Annual Review of Astronomy and Astrophysics]] | volume=8 |issue=1 |pages=265–296 |bibcode=1970ARA&A...8..265H |doi=10.1146/annurev.aa.08.090170.001405}}</ref> Until that time, neutron stars, like black holes, were regarded as just theoretical curiosities, but the discovery of pulsars showed their physical relevance and spurred a further interest in all types of compact objects that might be formed by gravitational collapse.<ref>{{cite web |url=https://www.smithsonianmag.com/science-nature/Fifty-years-ago-grad-students-discovery-changed-course-astrophysics-180968288/ |title=Fifty Years Ago, A Grad Student's Discovery Changed the Course of Astrophysics |date=28 February 2018 |access-date=22 December 2023 |website=Smithsonian Magazine |last=Boissoneault |first=Lorraine}}</ref> Based on observations in [[Royal Greenwich Observatory|Greenwich]] and [[David Dunlap Observatory|Toronto]] in the early 1970s, [[Cygnus X-1]], a galactic [[X-ray]] source discovered in 1964, became the first astronomical object commonly accepted to be a black hole.<ref name="rolston1997" /><ref name="Shipman1975">{{citation | last1=Shipman | first1=H. L. | date=1975 | title=The implausible history of triple star models for Cygnus&nbsp;X-1 Evidence for a black hole | journal=Astrophysical Letters | volume=16 | issue=1 | pages=9–12 | bibcode=1975ApL....16....9S | doi=10.1016/S0304-8853(99)00384-4 | last2=Yu | first2=Z | last3=Du | first3=Y.W }}</ref>

Work by [[James Bardeen]], [[Jacob Bekenstein]], Carter, and Hawking in the early 1970s led to the formulation of [[black hole thermodynamics]].<ref>{{cite journal |last1=Bardeen |first1=J. M. |author-link1=James M. Bardeen |last2=Carter |first2=B. |author-link2=Brandon Carter |last3=Hawking |first3=S. W. |author-link3=Stephen Hawking |date=1973 |title=The Four Laws of Black Hole Mechanics |journal=[[Communications in Mathematical Physics]] | volume=31 |issue=2 |pages=161–170 |doi=10.1007/BF01645742 |mr=0334798 |zbl=1125.83309 |bibcode=1973CMaPh..31..161B |s2cid=54690354 |url=http://projecteuclid.org/euclid.cmp/1103858973 |access-date=4 June 2021 |archive-date=16 May 2020 |archive-url=https://web.archive.org/web/20200516211604/https://projecteuclid.org/euclid.cmp/1103858973 |url-status=live }}</ref> These laws describe the behaviour of a black hole in a manner analogous to the [[laws of thermodynamics]]. Under this analogy, the properties of mass, [[surface area]], and [[surface gravity]] for a black hole are related to the thermodynamical concepts of energy, [[entropy]], and [[temperature]] respectively. The analogy was completed<ref name="Throne-1994" />{{rp|442}} when Hawking, in 1974, showed that [[quantum field theory]] implies that black holes should radiate like a [[black body]] with a temperature proportional to the surface gravity of the black hole, predicting the effect now known as [[Hawking radiation]].<ref name="Hawking1974">{{cite journal |last=Hawking |first=S. W. |author-link1=Stephen Hawking |title=Black Hole Explosions? |journal=Nature |date=1974 |volume=248 |issue=5443 |pages=30–31 |doi=10.1038/248030a0|bibcode=1974Natur.248...30H|s2cid=4290107 }}</ref>

=== Modern research and observation ===
[[File:LIGO measurement of gravitational waves.svg|upright=0.75|thumb|alt=Graphs of the first detections of gravitational waves at the Hanford and Livingston LIGO sections, along with comparisons to theoretical predictions, noise, and visual renderings. The readings appear as periodic waves that increase in magnitude over time before suddenly dropping back down. |The first detection of gravitational waves, imaged by LIGO observatories in [[Hanford Site]], Washington and [[Livingston, Louisiana]]]]While Cygnus X-1, a [[stellar-mass black hole]], was generally accepted by the scientific community as a black hole by the end of 1973,<ref name="rolston1997">{{cite web | last=Rolston | first=Bruce | date=10 November 1997 | url=http://news.utoronto.ca/bin/bulletin/nov10_97/art4.htm | title=The First Black Hole | publisher=University of Toronto | access-date=11 March 2008 | archive-url = https://web.archive.org/web/20080307181205/http://www.news.utoronto.ca/bin/bulletin/nov10_97/art4.htm | archive-date = 7 March 2008 }}</ref> it would be decades before a [[supermassive black hole]] would gain the same broad recognition. Although, as early as the 1960s, physicists such as [[Donald Lynden-Bell]] and [[Martin Rees]] had suggested that powerful [[quasars]] in the center of galaxies were powered by [[accretion (astrophysics)|accreting]] supermassive black holes, little observational proof existed at the time.<ref>{{Cite journal |last1=Lynden-Bell |first1=D. |title=Galactic Nuclei as Collapsed Old Quasars |journal=Nature |date=1969 |volume=223 |issue=5207 |pages=690–694 |doi=10.1038/223690a0 |bibcode=1969Natur.223..690L }}</ref><ref>{{Cite journal |last1= Rees|first1= Martin J.|title=Black Hole Models for Active Galactic Nuclei|journal= Annual Review of Astronomy and Astrophysics|date= 1984|volume= 22|pages= 471–506|doi=10.1146/annurev.aa.22.090184.002351|bibcode= 1984ARA&A..22..471R}}</ref> However, the [[Hubble Space Telescope]], launched in the 1990s, found that supermassive black holes were not only present in these [[active galactic nuclei]], but that supermassive black holes in the center of galaxies were ubiquitous: almost every galaxy had a supermassive black hole at its center. The black holes in quiescent galaxies accrete matter more slowly or radiate less efficiently.<ref name="ff05">{{Cite journal |last1=Ferrarese |first1=Laura |last2=Ford |first2=Holland |title=Supermassive Black Holes in Galactic Nuclei: Past, Present and Future Research |journal=Space Science Reviews |date=2005 |volume=116 |issue=3–4 |pages=523–624 |doi=10.1007/s11214-005-3947-6 |arxiv=astro-ph/0411247 |bibcode=2005SSRv..116..523F }}</ref><ref name="peterson14">{{Cite journal |last1=Peterson |first1=Bradley M. |title=Measuring the Masses of Supermassive Black Holes |journal=Space Science Reviews |date=2014 |volume=183 |issue=1–4 |pages=253–275 |doi=10.1007/s11214-013-9987-4 |bibcode=2014SSRv..183..253P }}</ref>

In 1999, [[David Merritt]] proposed the [[M–sigma relation]], which related the [[dispersion (statistics)|dispersion]] of the [[velocity]] of matter in the center [[galactic bulge|bulge]] of a galaxy to the mass of the supermassive black hole at its core.<ref>{{cite conference | first = David | last = Merritt | author-link = David Merritt | editor1-first = F. | editor1-last = Combes | editor2-first = G. A. | editor2-last = Mamon | editor3-first = V. | editor3-last = Charmandaris | title = Black holes and galaxy evolution | volume = 197 | book-title = Dynamics of Galaxies: from the Early Universe to the Present | publisher = [[Astronomical Society of the Pacific]] | pages = [https://archive.org/details/xvthiapmeetingdy0197iapm/page/221 221–232] | date = 1999 | isbn = 978-1-58381-024-8 | bibcode = 2000ASPC..197..221M | arxiv = astro-ph/9910546 | url = https://archive.org/details/xvthiapmeetingdy0197iapm/page/221 }}</ref> Subsequent studies confirmed this correlation.<ref>{{multiref2|{{Cite journal |display-authors=2 |last1=Tremaine |first1=Scott |last2=Gebhardt |first2=Karl |last3=Bender |first3=Ralf |last4=Bower |first4=Gary |last5=Dressler |first5=Alan |last6=Faber |first6=S. M. |last7=Filippenko |first7=Alexei V. |last8=Green |first8=Richard |last9=Grillmair |first9=Carl |last10=Ho |first10=Luis C. |last11=Kormendy |first11=John |last12=Lauer |first12=Tod R. |last13=Magorrian |first13=John |last14=Pinkney |first14=Jason |last15=Richstone |first15=Douglas |title=The Slope of the Black Hole Mass Versus Velocity Dispersion Correlation |journal=The Astrophysical Journal |date=2002 |volume=574 |issue=2 |pages=740–753 |doi=10.1086/341002 |arxiv=astro-ph/0203468 |bibcode=2002ApJ...574..740T }}|{{Cite journal |last1=Ferrarese |first1=Laura |last2=Merritt |first2=David |title=A Fundamental Relation Between Supermassive Black Holes and Their Host Galaxies |journal=The Astrophysical Journal |date=2000 |volume=539 |issue=1 |pages=L9–L12 |doi=10.1086/312838 |arxiv=astro-ph/0006053 |bibcode=2000ApJ...539L...9F }}|{{Cite journal |display-authors=2 |last1=Nelson |first1=Charles H. |last2=Green |first2=Richard F. |last3=Bower |first3=Gary |last4=Gebhardt |first4=Karl |last5=Weistrop |first5=Donna |title=The Relationship Between Black Hole Mass and Velocity Dispersion in Seyfert 1 Galaxies |journal=The Astrophysical Journal |date=2004 |volume=615 |issue=2 |pages=652–661 |doi=10.1086/424657 |arxiv=astro-ph/0407383 |bibcode=2004ApJ...615..652N }}}}</ref> Around the same time, based on telescope observations of the velocities of stars at the center of the Milky Way galaxy, independent work groups led by [[Andrea Ghez]] and [[Reinhard Genzel]] concluded that the compact [[astronomical radio source|radio source]] in the center of the galaxy, [[Sagittarius A*]], was likely a supermassive black hole.<ref>{{Cite journal |display-authors=2 |last1=Genzel |first1=R. |last2=Eckart |first2=A. |last3=Ott |first3=T. |last4=Eisenhauer |first4=F. |title=On the Nature of the Dark Mass in the Centre of the Milky Way |journal=Monthly Notices of the Royal Astronomical Society |date=1997 |volume=291 |pages=219–234 |doi=10.1093/mnras/291.1.219 |doi-access=free }}</ref><ref name="Ghez1998" />

In late 2015, the [[LIGO Scientific Collaboration]] and [[Virgo interferometer|Virgo Collaboration]] made the [[first observation of gravitational waves|first direct detection]] of [[gravitational wave]]s, named GW150914, representing the first observation of a [[black hole merger]].<ref name="PRL-20160211">{{cite journal |author=Abbott, B.P. |title=Observation of Gravitational Waves from a Binary Black Hole Merger |journal=[[Phys. Rev. Lett.]] | volume=116 |issue=6 |article-number=061102 |year=2016 |doi=10.1103/PhysRevLett.116.061102 |display-authors=etal |arxiv=1602.03837 |bibcode=2016PhRvL.116f1102A |pmid=26918975|s2cid=124959784 }}</ref> At the time of the merger, the black holes were approximately 1.4 billion [[light-years]] away from Earth and had masses roughly 30 and 35 times that of the Sun.<ref name="ligovirgo16">{{Cite journal|arxiv=1606.01210 |title=An Improved Analysis of GW150914 Using a Fully Spin-Precessing Waveform Model |journal=Physical Review X |volume=6 |issue=4 |article-number=041014 |author=The LIGO Scientific Collaboration and The Virgo Collaboration |doi=10.1103/PhysRevX.6.041014 |year=2016 |bibcode=2016PhRvX...6d1014A |s2cid=18217435 }}</ref>{{Rp|6}} In 2017, [[Rainer Weiss]], [[Kip Thorne]], and [[Barry Barish]], who had spearheaded the project, were awarded the Nobel Prize in Physics for their work.<ref>{{cite web |title=The Nobel Prize in Physics 2017 |publisher=Nobel Foundation |url=https://www.nobelprize.org/nobel_prizes/physics/laureates/2017/press.html }}</ref> Since the initial discovery in 2015, hundreds more gravitational waves have been observed.<ref>{{Cite web |title=LIGO-Virgo-KAGRA Announce the 200th Gravitational Wave Detection of O4! |url=https://www.ligo.caltech.edu/news/ligo20250320 |last=Burtnyk |first=Kimberly |date=20 March 2025 |access-date=22 October 2025 |website=LIGO Caltech}}</ref>

[[File:Black hole - Messier 87.jpg|thumb |alt=Over a black background of empty space, an orange-red donut of gas lies in the center of the image, with a black circle--the black hole's shadow--in the middle of the donut.|Image by the [[Event Horizon Telescope]] of the supermassive black hole in the center of [[Messier 87]]]]

On 10 April 2019, the first direct image of a black hole and its vicinity was published, following observations made by the [[Event Horizon Telescope]] (EHT) in 2017 of the supermassive black hole in [[Messier 87]]'s galactic centre.<ref name="APJL-20190410">{{cite journal|last1=Event Horizon Telescope|first1=The|author-link1=Event Horizon Telescope|date=2019|title=First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole|journal=[[The Astrophysical Journal]] | volume=875|page=L1|arxiv=1906.11238|bibcode=2019ApJ...875L...1E|doi=10.3847/2041-8213/ab0ec7|number=1|s2cid=145906806 |doi-access=free }}</ref> In 2022, the Event Horizon Telescope collaboration released an image of the black hole in the center of the Milky Way galaxy, Sagittarius A*; the data had been collected in 2017.<ref name="eht-press-release" />

In 2020, the [[Nobel Prize in Physics]] was awarded for work on black holes. [[Andrea Ghez]] and [[Reinhard Genzel]] shared one-half for their discovery that Sagittarius A* is a supermassive black hole.<ref>{{Cite web |title=2020 Nobel Prize in Physics |url=https://www.aps.org/archives/publications/apsnews/202011/nobel-physics.cfm |last=Poffenberger |first=Leah |access-date=20 October 2025 |website=American Physical Society}}</ref> Penrose received the other half for his work showing that the mathematics of general relativity requires the formation of black holes.<ref>{{cite web|title=The Nobel Prize in Physics 2020|url=https://www.nobelprize.org/prizes/physics/2020/summary/|access-date=8 October 2020|website=NobelPrize.org|archive-date=24 April 2021|archive-url=https://web.archive.org/web/20210424115309/https://www.nobelprize.org/prizes/physics/2020/summary/|url-status=live}}</ref> Cosmologists lamented that Hawking's extensive theoretical work on black holes would not be honoured since he had died in 2018.<ref>{{cite news |last1=Overbye |first1=Dennis| author-link1=Dennis Overbye |last2=Taylor |first2=Derrick Bryson |title=Nobel Prize in Physics Awarded to 3 Scientists for Work on Black Holes|url=https://www.nytimes.com/2020/10/06/science/nobel-prize-physics.html |date=6 October 2020 |work=[[The New York Times]] | access-date=6 October 2020 }}</ref>

=== Etymology ===
In December 1967, a student reportedly suggested the phrase ''black hole'' at a lecture by [[John Archibald Wheeler|John Wheeler]]; Wheeler adopted the term for its brevity and "advertising value", and Wheeler's stature in the field ensured it quickly caught on,<ref name="Bartusiak" /><ref>{{cite news |title=Pioneering Physicist John Wheeler Dies at 96 |url=https://www.scientificamerican.com/article/pioneering-physicist-john-wheeler-dies/ |access-date=27 November 2016 |work=[[Scientific American]] | url-status=live |archive-url=https://web.archive.org/web/20161128050759/https://www.scientificamerican.com/article/pioneering-physicist-john-wheeler-dies/ |archive-date=28 November 2016}}</ref> leading some to credit Wheeler with coining the phrase.<ref>{{cite news |last1=Overbye |first1=Dennis |title=John A. Wheeler, Physicist Who Coined the Term 'Black Hole,' Is Dead at 96 |url=https://www.nytimes.com/2008/04/14/science/14wheeler.html |access-date=27 November 2016 |work=[[The New York Times]] | date=14 April 2008 |url-status=live |archive-url=https://web.archive.org/web/20161122210005/http://www.nytimes.com/2008/04/14/science/14wheeler.html |archive-date=22 November 2016}}</ref> However, the term was used by others around that time. Science writer Marcia Bartusiak traces the term ''black hole'' to physicist [[Robert H. Dicke]], who in the early 1960s reportedly compared the phenomenon to the [[Black Hole of Calcutta]], notorious as a prison where people entered but never left alive.
The term was used in print by ''[[Life (magazine)|Life]]'' and ''[[Science News]]'' magazines in 1963, and by science journalist Ann Ewing in her article {{" '}}Black Holes' in Space", dated 18 January 1964, which was a report on a meeting of the [[American Association for the Advancement of Science]] held in Cleveland, Ohio.<ref name="Bartusiak">{{cite book |last=Bartusiak |first=Marcia |author-link=Marcia Bartusiak |title=Black Hole: How an Idea Abandoned by Newtonians, Hated by Einstein, And Gambled On by Hawking Became Loved |date=2015 |publisher=[[Yale University Press]] | isbn=978-0-300-21363-8}}</ref>

== Definition ==
A black hole is generally defined as a region of spacetime from which no [[Randomness#In the physical sciences|information-carrying]] signals or objects can escape.<ref name="fz11">{{Cite book |title=Introduction to Black Hole Physics |last1=Frolov |first1=Valeri P. |date=1 December 2011 |publisher=Oxford University Press |isbn=978-0-19-969229-3 |edition=1st |page=1 |last2=Zelnikov |first2=Andrei}}</ref> However, verifying an object as a black hole by this definition would require waiting for an infinite time and at an infinite distance from the black hole to verify that indeed, nothing has escaped, and thus cannot be used to identify a physical black hole.<ref name="booth05">{{Cite journal |last1=Booth |first1=Ivan |title=Black-hole boundaries |journal=Canadian Journal of Physics |date=2005 |volume=83 |issue=11 |pages=1073–1099 |doi=10.1139/p05-063 |arxiv=gr-qc/0508107 |bibcode=2005CaJPh..83.1073B }}</ref> There are several other definitions that can be used to describe or identify a black hole, although they are not universally agreed upon by physicists. Among astrophysicists, a black hole is a [[compact object]] with a mass larger than four solar masses.<ref name="curiel19">{{Cite journal |last1=Curiel |first1=Erik |title=The many definitions of a black hole |journal=Nature Astronomy |date=2019 |volume=3 |pages=27–34 |doi=10.1038/s41550-018-0602-1 |arxiv=1808.01507 |bibcode=2019NatAs...3...27C }}</ref> A black hole may also be defined as a reservoir of information<ref name="bhwar">{{cite book |last=Susskind |first=Leonard |author-link=Leonard Susskind |title=The black hole war: my battle with Stephen Hawking to make the world safe for quantum mechanics |title-link=The Black Hole War |date=2008 |publisher=Little, Brown |isbn=978-0-316-01640-7 |edition=1st |oclc=181603165}}</ref>{{rp|142}} or a region where space is falling inwards faster than the speed of light.<ref>{{Cite journal |last1=Hamilton |first1=Andrew J. S. |last2=Lisle |first2=Jason P. |date=June 1, 2008 |title=The river model of black holes |url=https://pubs.aip.org/ajp/article/76/6/519/237222/The-river-model-of-black-holes |journal=American Journal of Physics |language=en |volume=76 |issue=6 |pages=519–532 |doi=10.1119/1.2830526 |arxiv=gr-qc/0411060 |bibcode=2008AmJPh..76..519H |issn=0002-9505}}</ref><ref name="waterfall">{{Cite web |title=A Black Hole is a Waterfall of Space |url=https://jila.colorado.edu/~ajsh/insidebh/waterfall.html |last=Hamilton |first=Andrew |url-status=live |archive-url=https://web.archive.org/web/20250820063124/https://jila.colorado.edu/%7Eajsh/insidebh/waterfall.html |archive-date=20 August 2025 |access-date=24 October 2025 |website=Inside Black Holes}}</ref>

== Properties ==
The [[no-hair theorem]] postulates that, once it achieves a stable condition after formation, a black hole has only three independent physical properties: mass, electric charge, and angular momentum; the black hole is otherwise featureless. If the conjecture is true, any two black holes that share the same values for these properties, or parameters, are indistinguishable from one another. The degree to which the conjecture is true is currently an unsolved problem.<ref name="HeuslerNoHair">{{cite journal |vauthors=Chruściel PT, Costa JL, Heusler M |date=2012 |title=Stationary Black Holes: Uniqueness and Beyond |journal=[[Living Reviews in Relativity]] | type=Article |volume=15 |issue=7 |arxiv=1205.6112 |bibcode=2012LRR....15....7C |doi=10.12942/lrr-2012-7 |pmc=5255892 |pmid=28179837 |doi-access=free |article-number=7}}</ref><ref>{{Cite journal |last1=Yang |first1=Xilong |last2=Tang |first2=Meirong |last3=Xu |first3=Zhaoyi |title=Exploring the Possibility of Testing the No-Hair Theorem with Minkowski-Deformed Regular Hairy Black Holes via Photon Rings |journal=The European Physical Journal C |date=2024 |volume=84 |issue=9 |article-number=977 |doi=10.1140/epjc/s10052-024-13343-y |doi-access=free }}</ref>

The simplest static black holes, called ''Schwarzschild black holes'', have mass but neither electric charge nor angular momentum. 
Non-rotating [[charged black hole]]s are described by the [[Reissner–Nordström metric]], while the [[Kerr metric]] describes a non-charged [[rotating black hole]]. The most general [[stationary spacetime|stationary]] black hole solution known is the [[Kerr–Newman metric]], which describes a black hole with both charge and angular momentum.<ref name="shapiro_teukolsky1983">{{cite book |last1=Shapiro |first1=S. L. |last2=Teukolsky |first2=S. A. |author2-link=Saul Teukolsky |title=Black Holes, White Dwarfs, And Neutron Stars: The Physics of Compact Objects |page=357 |publisher=John Wiley and Sons |date=1983 |isbn=978-0-471-87316-7}}</ref>

=== Mass ===
[[File:Black Hole Shadow.ogg|thumbtime=0|thumb|alt=A black hole's Schwarzschild radius is described by the equation r sub s equals two G M over c squared. The radius of its shadow is described by the equation R equals square root of 27 over 2 r sub s approximately equals 2.6 r sub s. The radius of its photon sphere is described by the equation R equals 1.5 r sub s.|Radii for shadow and photon sphere relative to the event horizon]]

The simplest static black holes have mass but neither electric charge nor angular momentum. Contrary to the popular notion of a black hole "sucking in everything" in its surroundings, from far away, the external gravitational field of a black hole is identical to that of any other body of the same mass.<ref>{{cite book |first1=Michael A. |last1=Seeds |first2=Dana E. |last2=Backman |title=Perspectives on Astronomy |page=167 |publisher=Cengage Learning |date=2007 |isbn=978-0-495-11352-2 |url=https://books.google.com/books?id=CXom04KGIL8C&pg=PA167|url-status=live |archive-url=https://web.archive.org/web/20160810211808/https://books.google.com/books?id=CXom04KGIL8C&pg=PA167 |archive-date=10 August 2016}}</ref>

While a black hole can theoretically have any positive mass, its charge and angular momentum are limited by its mass, with this limit being greater for more massive black holes. The net electric charge <math>Q</math> and the total angular momentum <math>J</math> satisfy the inequality
<math display="block">\frac{Q^2}{4\pi\epsilon_0} + \frac{c^2 J^2}{G M^2} \le G M^2</math>
for a black hole of mass <math>M</math>, where <math>\epsilon_0</math> is the [[vacuum permittivity]] constant, <math>c</math> is the [[speed of light]] and <math>G</math> is the [[gravitational constant]]. Black holes with the maximum possible combination of charge and spin satisfying this inequality are called [[extremal black holes]]. Solutions of Einstein's equations that violate this inequality exist, but they do not possess an event horizon. These are so-called [[naked singularity|naked singularities]] that can be observed from the outside.<ref name="wald 1997">{{cite book |last=Wald |first=R. M. |author-link=Robert Wald |title=Black Holes, Gravitational Radiation and the Universe |editor1=Iyer, B. R. |editor2=Bhawal, B. |chapter=Gravitational Collapse and Cosmic Censorship |arxiv=gr-qc/9710068 |date=1997 |pages=69–86|publisher=Springer |doi=10.1007/978-94-017-0934-7 |isbn=978-94-017-0934-7}}</ref> Because these singularities make the universe inherently unpredictable, many physicists believe they could not exist.<ref>{{cite journal |last=Berger |first=B. K.|author-link= Beverly Berger |date=2002 |title=Numerical Approaches to Spacetime Singularities |journal=Living Reviews in Relativity |volume=5 |issue=1 |pages=2002–1|article-number=1 |bibcode=2002LRR.....5....1B |doi=10.12942/lrr-2002-1 |doi-access=free |pmid=28179859 |pmc=5256073 |arxiv=gr-qc/0201056}}</ref> The [[weak cosmic censorship hypothesis]], proposed by Penrose, rules out the formation of such singularities, when they are created through the gravitational collapse of [[energy conditions|realistic matter]]. However, this theory has not yet been proven, and some physicists believe that naked singularities could exist.<ref name="joshi09">{{Cite magazine |date=1 February 2009 |title=Naked Singularities |magazine=[[Scientific American]] | last=Joshi |first=Pankaj S.  |pages=36–43 |volume=300 |issue=2 |jstor=26001219 }}</ref> It is also unknown whether black holes could even become extremal, forming naked singularities, since natural processes counteract increasing spin and charge when a black hole becomes near-extremal.<ref>{{Cite journal |last1=Ghosh |first1=Rajes |last2=Mishra |first2=Akash K. |last3=Sarkar |first3=Sudipta |title=Overcharging Extremal Black Holes |journal=Physical Review D |date=2021 |volume=104 |issue=10 |article-number=104043 |doi=10.1103/PhysRevD.104.104043 |arxiv=2106.10667 |bibcode=2021PhRvD.104j4043G }}</ref>

The total mass of a black hole can be estimated by analysing the motion of objects near the black hole, such as stars or gas.<ref name="peterson14" />

=== Spin and angular momentum ===
All black holes spin, often fast—One stellar black hole, [[GRS 1915+105]], has been estimated to spin at over 1,000 revolutions per second.<ref>{{Cite web |title=Black Hole Basics |url=https://science.nasa.gov/universe/black-holes/ |access-date=25 October 2025 |website=NASA.gov |date=13 March 2024 }}</ref> The Milky Way's central black hole Sagittarius A* rotates at about 90% of the maximum possible rate.<ref name="daly19">{{Cite journal |last1=Daly |first1=Ruth A. |title=Black Hole Spin and Accretion Disk Magnetic Field Strength Estimates for More Than 750 Active Galactic Nuclei and Multiple Galactic Black Holes |journal=The Astrophysical Journal |date=2019 |volume=886 |issue=1 |page=37 |doi=10.3847/1538-4357/ab35e6 |arxiv=1905.11319 |bibcode=2019ApJ...886...37D |doi-access=free }}</ref><ref>{{Cite journal |display-authors=2 |last1=Daly |first1=Ruth A. |last2=Donahue |first2=Megan |last3=o'Dea |first3=Christopher P. |last4=Sebastian |first4=Biny |last5=Haggard |first5=Daryl |last6=Lu |first6=Anan |title=New Black Hole Spin Values for Sagittarius A* Obtained with the Outflow Method |journal=Monthly Notices of the Royal Astronomical Society |date=2024 |volume=527 |pages=428–436 |doi=10.1093/mnras/stad3228 |doi-access=free }}</ref>

The spin rate can be inferred from measurements of atomic [[spectral line]]s in the X-ray range. As gas near the black hole plunges inward, high energy X-ray emission from electron-positron pairs illuminates the gas further out, appearing red-shifted due to relativistic effects. Depending on the spin of the black hole, this plunge happens at different radii from the hole, with different degrees of redshift. Astronomers can use the gap between the x-ray emission of the outer disk and the redshifted emission from plunging material to determine the spin of the black hole.<ref name="reynolds19">{{Cite journal|last=Reynolds|first=Christopher S.|date=January 2019|title=Observing Black Holes Spin|url=https://www.nature.com/articles/s41550-018-0665-z|journal=Nature Astronomy|volume=3|issue=1|pages=41–47|doi=10.1038/s41550-018-0665-z|issn=2397-3366|arxiv=1903.11704|bibcode=2019NatAs...3...41R|s2cid=85543351|access-date=21 August 2020|archive-date=18 November 2020|archive-url=https://web.archive.org/web/20201118092121/https://www.nature.com/articles/s41550-018-0665-z|url-status=live}}</ref>

A newer way to estimate spin is based on the temperature of gases accreting onto the black hole. The method requires an independent measurement of the black hole mass and [[orbital inclination|inclination angle]] of the accretion disk followed by computer modelling. Gravitational waves from coalescing binary black holes can also provide the spin of both progenitor black holes and the merged hole, but such events are rare.<ref name="reynolds19" />

A spinning black hole has [[angular momentum]]. The supermassive black hole in the center of the [[Messier 87]] (M87) galaxy appears to have an angular momentum very close to the maximum theoretical value.<ref>{{Cite journal |last1=Tamburini |first1=Fabrizio |last2=Thidé |first2=Bo |last3=Della Valle |first3=Massimo |title=Measurement of the Spin of the M87 Black Hole from Its Observed Twisted Light |journal=Monthly Notices of the Royal Astronomical Society: Letters |date=2020 |volume=492 |pages=L22–L27 |doi=10.1093/mnrasl/slz176 |doi-access=free |arxiv=1904.07923 }}</ref><ref>{{Cite journal |display-authors=2 |last1=Bambi |first1=Cosimo |last2=Freese |first2=Katherine |last3=Vagnozzi |first3=Sunny |last4=Visinelli |first4=Luca |title=Testing the Rotational Nature of the Supermassive Object M87* from the Circularity and Size of Its First Image |journal=Physical Review D |date=2019 |volume=100 |issue=4 |article-number=044057 |doi=10.1103/PhysRevD.100.044057 |arxiv=1904.12983 |bibcode=2019PhRvD.100d4057B }}</ref> By setting <math>Q</math> equal to 0, the maximum spin of an uncharged black hole can be simplified to<ref name="50SMBH">{{cite journal |doi=10.1103/PhysRevLett.118.221101 |pmid=28621973 |title=GW170104: Observation of a 50-Solar-Mass Binary Black Hole Coalescence at Redshift 0.2 |journal=[[Physical Review Letters]] | date=1 June 2017 |first=B. P. |last=Abbott |collaboration=[[LIGO Scientific Collaboration]] and Virgo Collaboration |volume=118 |issue=22 |article-number=221101 |arxiv=1706.01812 |bibcode=2017PhRvL.118v1101A|s2cid=206291714 }}</ref>
<math display="block">J \le \frac{GM^{2}}{c},</math>
allowing definition of a [[dimensionless]] spin magnitude such that<ref name="50SMBH" /><ref>{{Cite journal |last1=Horbatsch |first1=M.W |last2=Burgess |first2=C.P |title=Cosmic Black-Hole Hair Growth and Quasar OJ287 |journal=Journal of Cosmology and Astroparticle Physics |date=2012 |issue=5 |page=010 |doi=10.1088/1475-7516/2012/05/010 |arxiv=1111.4009 |bibcode=2012JCAP...05..010H }}</ref>
<math display="block"> 0 \le \frac{cJ}{GM^{2}}\le 1.</math>

=== Charge ===
Most black holes are believed to have an approximately neutral charge. For example, Michal Zajaček, Arman Tursunov, Andreas Eckart, and Silke Britzen found the [[electric charge]] of Sagittarius A* to be at least ten orders of magnitude below the theoretical maximum.<ref name="zteb18" /> A charged black hole [[Coulomb's law|repels]] other like charges just like any other charged object.<ref>{{Cite journal |last1=Xu |first1=Hao |last2=Ong |first2=Yen Chin |last3=Yung |first3=Man-Hong |title=Cosmic Censorship and the Evolution of <math>d</math> -Dimensional Charged Evaporating Black Holes |journal=Physical Review D |date=2020 |volume=101 |issue=6 |article-number=064015 |doi=10.1103/PhysRevD.101.064015 |arxiv=1911.11990 |bibcode=2020PhRvD.101f4015X }}</ref> If a black hole were to become charged, particles with an opposite sign of charge would be pulled in by the extra [[electromagnetism|electromagnetic force]], while particles with the same sign of charge would be repelled, neutralising the black hole. This effect may not be as strong if the black hole is also spinning.<ref>{{Cite journal |display-authors=2 |last1=Gong |first1=Yi |last2=Cao |first2=Zhoujian |last3=Gao |first3=He |last4=Zhang |first4=Bing |title=On Neutralization of Charged Black Holes |journal=Monthly Notices of the Royal Astronomical Society |date=2019 |volume=488 |issue=2 |pages=2722–2731 |doi=10.1093/mnras/stz1904 |doi-access=free |arxiv=1907.05239 }}</ref> The presence of charge can reduce the diameter of the black hole's shadow by up to 38%.<ref name="zteb18">{{Cite journal |display-authors=2 |last1=Zajaček |first1=Michal |last2=Tursunov |first2=Arman |last3=Eckart |first3=Andreas |last4=Britzen |first4=Silke |title=On the Charge of the Galactic Centre Black Hole |journal=Monthly Notices of the Royal Astronomical Society |date=2018 |volume=480 |issue=4 |pages=4408–4423 |doi=10.1093/mnras/sty2182 |doi-access=free |arxiv=1808.07327 }}</ref><ref>{{Cite journal |display-authors=2 |last1=Zakharov |first1=A. F. |last2=De Paolis |first2=F. |last3=Ingrosso |first3=G. |last4=Nucita |first4=A. A. |title=Direct Measurements of Black Hole Charge with Future Astrometrical Missions |journal=Astronomy & Astrophysics |date=2005 |volume=442 |issue=3 |pages=795–799 |doi=10.1051/0004-6361:20053432 |arxiv=astro-ph/0505286 |bibcode=2005A&A...442..795Z }}</ref>

The charge Q for a nonspinning black hole is bounded by
<math display="block">Q\leq\sqrt{4\pi \epsilon_0 G}M,</math>
where G is the gravitational constant and M is the black hole's mass.<ref>{{Cite journal |display-authors=2 |last1=Turimov |first1=Bobur |last2=Boboqambarova |first2=Madina |last3=Ahmedov |first3=Bobomurat |last4=Stuchlík |first4=Zdeněk |title=Distinguishable Feature of Electric and Magnetic Charged Black Hole |journal=The European Physical Journal Plus |date=2022 |volume=137 |issue=2 |article-number=222 |doi=10.1140/epjp/s13360-022-02390-7}}</ref>

== Classification ==
{| class="wikitable" style="float:right; margin:0 0 0.5em 1em;"
|+ Black hole classifications
|-
! Class !! Approx.<br />mass !! Approx.<br />radius
|-
| [[Supermassive black hole#Ultramassive black holes|Ultramassive black hole]] ||style="text-align: center;" | {{10^|9}}–{{solar mass|{{10^|11}}}}  ||style="text-align: center;" | >1,000 [[Astronomical unit|AU]]
|-
| [[Supermassive black hole]] ||style="text-align: center;" | {{10^|6}}–{{solar mass|{{10^|9}}}} ||style="text-align: center;" | 0.001–400 [[Astronomical unit|AU]]
|-
| [[Intermediate-mass black hole]]<ref name="mc04" /> ||style="text-align: center;" | {{10^|2}}–{{solar mass|{{10^|5}}}} ||style="text-align: center;" | 10{{sup|3}} km ≈ [[Earth radius|''R''{{sub|Earth}}]]
|-
| [[Stellar black hole]] ||style="text-align: center;" | {{solar mass|2–150}} ||style="text-align: center;" | 30&nbsp;km
|-
| [[Micro black hole]] ||style="text-align: center;" | up to ''M''{{sub|[[Moon]]}} ||style="text-align: center;" | up to 0.1&nbsp;mm
|}
Black holes are classified by the theory of their formation and by their mass (expressed in terms of {{solar mass}}, the mass of the Sun), but these criteria are intertwined. [[Stellar black holes]] are formed by stellar collapse. The minimum mass of a black hole formed by stellar gravitational collapse is governed by the maximum mass of a neutron star and is believed to be {{solar mass|2-4}}.<ref>{{multiref2 |{{Cite journal  |last1=Cromartie |first1=H. T. |last2=Fonseca |first2=E. |last3=Ransom |first3=S. M. |last4=Demorest |first4=P. B. |last5=Arzoumanian |first5=Z. |last6=Blumer |first6=H. |last7=Brook |first7=P. R. |last8=Decesar |first8=M. E. |last9=Dolch |first9=T. |last10=Ellis |first10=J. A. |last11=Ferdman |first11=R. D. |last12=Ferrara |first12=E. C. |last13=Garver-Daniels |first13=N. |last14=Gentile |first14=P. A. |last15=Jones |first15=M. L. |last16=Lam |first16=M. T. |last17=Lorimer |first17=D. R. |last18=Lynch |first18=R. S. |last19=McLaughlin |first19=M. A. |last20=Ng |first20=C. |last21=Nice |first21=D. J. |last22=Pennucci |first22=T. T. |last23=Spiewak |first23=R. |last24=Stairs |first24=I. H. |last25=Stovall |first25=K. |last26=Swiggum |first26=J. K. |last27=Zhu |first27=W. W. |title=Relativistic Shapiro Delay Measurements of an Extremely Massive Millisecond Pulsar |journal=Nature Astronomy |date=2019 |volume=4 |pages=72–76 |doi=10.1038/s41550-019-0880-2 |arxiv=1904.06759 |display-authors=2}}|{{Cite journal |last1=Drischler |first1=Christian |last2=Han |first2=Sophia |last3=Lattimer |first3=James M. |last4=Prakash |first4=Madappa |last5=Reddy |first5=Sanjay |last6=Zhao |first6=Tianqi |title=Limiting Masses and Radii of Neutron Stars and Their Implications |journal=Physical Review C |date=2021 |volume=103 |issue=4 |article-number=045808 |doi=10.1103/PhysRevC.103.045808 |arxiv=2009.06441 |bibcode=2021PhRvC.103d5808D |display-authors=2}}|{{Cite journal |last1=Farr |first1=Will M. |last2=Sravan |first2=Niharika |last3=Cantrell |first3=Andrew |last4=Kreidberg |first4=Laura |last5=Bailyn |first5=Charles D. |last6=Mandel |first6=Ilya |last7=Kalogera |first7=Vicky |title=The Mass Distribution of Stellar-Mass Black Holes |journal=The Astrophysical Journal |date=2011 |volume=741 |issue=2 |page=103 |doi=10.1088/0004-637X/741/2/103 |arxiv=1011.1459 |bibcode=2011ApJ...741..103F |display-authors=2}}}}</ref> Hypothetical [[primordial black hole]]s, believed to have formed soon after the [[Big Bang]], could be far smaller, with masses as little as {{val|e=-5|u=grams}} at formation.<ref name="Carr">{{Cite journal |display-authors=2 |last1=Carr |first1=Bernard |last2=Kohri |first2=Kazunori |last3=Sendouda |first3=Yuuiti |last4=Yokoyama |first4=Jun'Ichi |title=Constraints on Primordial Black Holes |journal=Reports on Progress in Physics |date=2021 |volume=84 |issue=11 |doi=10.1088/1361-6633/ac1e31 |pmid=34874316 |arxiv=2002.12778 |bibcode=2021RPPh...84k6902C }}</ref> These very small black holes are sometimes called [[micro black hole]]s.<ref>{{Cite journal |last1=Nakama |first1=Tomohiro |last2=Yokoyama |first2=Jun'Ichi |title=Micro Black Holes Formed in the Early Universe and Their Cosmological Implications |journal=Physical Review D |date=2019 |volume=99 |issue=6 |article-number=061303 |doi=10.1103/PhysRevD.99.061303 |arxiv=1811.05049 |bibcode=2019PhRvD..99f1303N }}</ref><ref>{{Cite journal |last1=Scardigli |first1=Fabio |title=Gravity Coupling from Micro-Black Holes |journal=Nuclear Physics B – Proceedings Supplements |date=2000 |volume=88 |issue=1–3 |pages=291–294 |doi=10.1016/S0920-5632(00)00788-X |arxiv=hep-th/9907150 |bibcode=2000NuPhS..88..291S }}</ref>

Stellar black holes can have a wide range of masses. Estimates of their maximum mass at formation vary, but generally range from {{solar mass|10-100}}, with higher estimates for black holes progenated by [[metallicity|low-metallicity]] stars.<ref name=Vink-2021>{{Cite journal |display-authors=2 |last1=Vink |first1=Jorick S. |last2=Higgins |first2=Erin R. |last3=Sander |first3=Andreas A C. |last4=Sabhahit |first4=Gautham N. |title=Maximum Black Hole Mass Across Cosmic Time |journal=Monthly Notices of the Royal Astronomical Society |date=2021 |volume=504 |pages=146–154 |doi=10.1093/mnras/stab842 |doi-access=free |arxiv=2010.11730 }}</ref> Stellar black holes can gain mass via accretion of nearby matter, often from a companion object such as a star<ref name="lph97">{{Cite journal |display-authors=2 |last1=Dunn |first1=R. J. H. |last2=Fender |first2=R. P. |last3=Körding |first3=E. G. |last4=Belloni |first4=T. |last5=Cabanac |first5=C. |title=A Global Spectral Study of Black Hole X-Ray Binaries |journal=Monthly Notices of the Royal Astronomical Society |date=2010 |volume=403 |issue=1 |pages=61–82 |doi=10.1111/j.1365-2966.2010.16114.x |arxiv=0912.0142 |bibcode=2010MNRAS.403...61D |doi-access=free }}</ref><ref>{{Cite journal|last1=Shao |first1=Yong |last2=Li |first2=Xiang-Dong |title=Population Synthesis of Black Hole X-Ray Binaries |journal=The Astrophysical Journal |date=2020 |volume=898 |issue=2 |page=143 |doi=10.3847/1538-4357/aba118 |arxiv=2006.15961 |bibcode=2020ApJ...898..143S |doi-access=free }}</ref> or by merger with another black hole.<ref name="PRL-20160211"/>

Black holes that are larger than stellar black holes but smaller than supermassive black holes are called [[intermediate-mass black hole]]s, with approximately {{solar mass|{{value|e=2}}-{{value|e=5}}}}. These black holes seem to be rarer than their stellar and supermassive counterparts, with only a small number of candidates observed so far.<ref name="mc04">{{Cite journal |last1=Coleman Miller |first1=M. |last2=Colbert |first2=E. J. M. |title=Intermediate-Mass Black Holes |journal=International Journal of Modern Physics D |date=2004 |volume=13 |issue=1 |pages=1–64 |doi=10.1142/S0218271804004426 |arxiv=astro-ph/0308402 |bibcode=2004IJMPD..13....1M }}</ref> Physicists have speculated that such black holes may form from collisions in [[globular cluster|globular]] and [[star cluster|star]] clusters or at the center of [[dwarf galaxy|low-mass galaxies]].<ref>{{multiref2|{{Cite journal |last1=Coleman Miller |first1=M. |last2=Hamilton |first2=Douglas P. |title=Production of Intermediate-Mass Black Holes in Globular Clusters |journal=Monthly Notices of the Royal Astronomical Society |date=2002 |volume=330 |issue=1 |pages=232–240 |doi=10.1046/j.1365-8711.2002.05112.x |arxiv=astro-ph/0106188 |bibcode=2002MNRAS.330..232C |doi-access=free }}|{{Cite journal |display-authors=2 |last1=Rizzuto |first1=Francesco Paolo |last2=Naab |first2=Thorsten |last3=Spurzem |first3=Rainer |last4=Giersz |first4=Mirek |last5=Ostriker |first5=J. P. |last6=Stone |first6=N. C. |last7=Wang |first7=Long |last8=Berczik |first8=Peter |last9=Rampp |first9=M. |title=Intermediate Mass Black Hole Formation in Compact Young Massive Star Clusters |journal=Monthly Notices of the Royal Astronomical Society |date=2021 |volume=501 |issue=4 |pages=5257–5273 |doi=10.1093/mnras/staa3634 |doi-access=free |arxiv=2008.09571 }}|{{Cite journal |last1=Barai |first1=Paramita |last2=De Gouveia Dal Pino |first2=Elisabete M. |title=Intermediate-Mass Black Hole Growth and Feedback in Dwarf Galaxies at High Redshifts |journal=Monthly Notices of the Royal Astronomical Society |date=2019 |volume=487 |issue=4 |pages=5549–5563 |doi=10.1093/mnras/stz1616 |doi-access=free |arxiv=1807.04768 }}}}</ref> They may also form as the result of mergers of smaller black holes, with several LIGO observations finding merged black holes within {{solar mass|110–350}}.<ref>{{Cite journal |display-authors=2 |last1=Ruiz-Rocha |first1=Krystal |last2=Yelikar |first2=Anjali B. |last3=Lange |first3=Jacob |last4=Gabella |first4=William |last5=Weller |first5=Robert A. |last6=o'Shaughnessy |first6=Richard |last7=Holley-Bockelmann |first7=Kelly |last8=Jani |first8=Karan |title=Properties of "Lite" Intermediate-Mass Black Hole Candidates in LIGO-Virgo's Third Observing Run |journal=The Astrophysical Journal Letters |date=2025 |volume=985 |issue=2 |pages=L37 |doi=10.3847/2041-8213/adc5f8 |arxiv=2502.17681 |bibcode=2025ApJ...985L..37R |doi-access=free }}</ref><ref>{{Cite journal |display-authors=2 |last1=Abbott |first1=R. |last2=Abbott |first2=T. D. |last3=Acernese |first3=F. |last4=Ackley |first4=K. |last5=Adams |first5=C. |last6=Adhikari |first6=N. |last7=Adhikari |first7=R. X. |last8=Adya |first8=V. B. |last9=Affeldt |first9=C. |last10=Agarwal |first10=D. |last11=Agathos |first11=M. |last12=Agatsuma |first12=K. |last13=Aggarwal |first13=N. |last14=Aguiar |first14=O. D. |last15=Aiello |first15=L. |last16=Ain |first16=A. |last17=Ajith |first17=P. |last18=Akutsu |first18=T. |last19=Albanesi |first19=S. |last20=Allocca |first20=A. |last21=Altin |first21=P. A. |last22=Amato |first22=A. |last23=Anand |first23=C. |last24=Anand |first24=S. |last25=Ananyeva |first25=A. |last26=Anderson |first26=S. B. |last27=Anderson |first27=W. G. |last28=Ando |first28=M. |last29=Andrade |first29=T. |last30=Andres |first30=N. |title=Search for Intermediate-Mass Black Hole Binaries in the Third Observing Run of Advanced LIGO and Advanced Virgo |journal=Astronomy & Astrophysics |date=2022 |volume=659 |pages=A84 |doi=10.1051/0004-6361/202141452 |arxiv=2105.15120 |bibcode=2022A&A...659A..84A }}</ref>

The black holes with the largest masses are called [[supermassive black hole]]s, with masses more than {{solar mass|{{value|e=6}}}}.<ref>{{Cite book |last1=Mezcua |first1=Mar |title=Encyclopedia of Astrobiology |chapter=Black Holes |date=2021 |pages=1–8 |doi=10.1007/978-3-642-27833-4_5510-1 |arxiv=2110.08629 |isbn=978-3-642-27833-4 }}</ref> These black holes are believed to exist at the centers of almost every large galaxy, including the Milky Way.<ref name="ff05" /><ref name="peterson14" /> Some scientists have proposed a subcategory of even larger black holes, called [[ultramassive black hole]]s, with masses greater than {{solar mass|{{value|e=9}}-{{value|e=10}}}}.<ref>{{Cite journal |last1=Natarajan |first1=Priyamvada |last2=Treister |first2=Ezequiel |title=Is There an Upper Limit to Black Hole Masses? |journal=Monthly Notices of the Royal Astronomical Society |date=2009 |volume=393 |issue=3 |pages=838–845 |doi=10.1111/j.1365-2966.2008.13864.x |arxiv=0808.2813 |bibcode=2009MNRAS.393..838N |doi-access=free }}</ref><ref>{{Cite journal |last1=Dullo |first1=Bililign T. |last2=Gil De Paz |first2=Armando |last3=Knapen |first3=Johan H. |title=Ultramassive Black Holes in the Most Massive Galaxies: M <sub>BH</sub>–σ Versus M <sub>BH</sub>–R <sub>b</sub> |journal=The Astrophysical Journal |date=2021 |volume=908 |issue=2 |page=134 |doi=10.3847/1538-4357/abceae |arxiv=2012.04471 |bibcode=2021ApJ...908..134D |doi-access=free }}</ref> Theoretical models predict that the accretion disc that feeds black holes will be unstable once a black hole reaches {{solar mass|{{val|50|e=9}}–{{val|100|e=9}}}}, setting a rough upper limit to black hole mass.<ref>{{cite journal | title=How big can a black hole grow? | last1=King | first1=Andrew | journal=Monthly Notices of the Royal Astronomical Society: Letters | volume=456 | issue=1 | pages=L109–L112 | date=February 2016 | doi=10.1093/mnrasl/slv186 | doi-access=free | bibcode=2016MNRAS.456L.109K | arxiv=1511.08502 | s2cid=40147275 }}</ref><ref>{{cite web | url=https://www.science.org/content/article/limit-how-big-black-holes-can-grow-astonishing | title=Limit to how big black holes can grow is astonishing | first1=Daniel | last1=Clery | date=December 21, 2015 | website=sciencemag.org | access-date=November 27, 2018}}</ref>

== Structure ==

While black holes are conceptually invisible sinks of all matter and light, in astronomical settings, their enormous gravity alters the motion of surrounding objects and pulls nearby gas inwards at near-light speed, making the area around black holes the brightest objects in the universe.<ref name="reynolds21">{{Cite journal |last=Reynolds |first=Christopher S. |date=September 8, 2021 |title=Observational Constraints on Black Hole Spin |url=https://www.annualreviews.org/doi/10.1146/annurev-astro-112420-035022 |journal=Annual Review of Astronomy and Astrophysics |language=en |volume=59 |issue=1 |pages=117–154 |doi=10.1146/annurev-astro-112420-035022 |arxiv=2011.08948 |bibcode=2021ARA&A..59..117R |issn=0066-4146}}</ref>

=== External geometry ===
==== Relativistic jets ====
{{See also|Astrophysical jet}}
[[File:Black Hole Outflows From Centaurus A.jpg|thumb |alt=See caption. |Relativistic jets from the supermassive black hole in [[Centaurus A]] extend [[perpendicular]]ly from the galaxy.]]
Some black holes have relativistic jets—thin streams of [[plasma (physics)|plasma]] travelling away from the black hole at more than one-tenth of the speed of light.<ref name="mr99">{{Cite journal |last1=Mirabel |first1=I. F. |last2=Rodríguez |first2=L. F. |title=Sources of Relativistic Jets in the Galaxy |journal=Annual Review of Astronomy and Astrophysics |date=1999 |volume=37 |pages=409–443 |doi=10.1146/annurev.astro.37.1.409 |arxiv=astro-ph/9902062 |bibcode=1999ARA&A..37..409M }}</ref> A small fraction of the matter falling towards the black hole gets accelerated away along the hole rotation axis.<ref>{{Cite web |title=Relativistic Jets |url=https://nustar.caltech.edu/page/relativistic-jets |access-date=2025-11-09 |website=NuSTAR}}</ref> These jets can extend as far as millions of [[light-year]]s from the black hole itself.<ref>{{Cite journal |display-authors=2 |last9=Jacob |first9=Joe |last1=Bagchi |first1=Joydeep |last2=Vivek |first2=M. |last3=Vikram |first3=Vinu |last4=Hota |first4=Ananda |last5=Biju |first5=K. G. |last6=Sirothia |first6=S. K. |last7=Srianand |first7=Raghunathan |last8=Gopal-Krishna |title=Megaparsec Relativistic Jets Launched from an Accreting Supermassive Black Hole in an Extreme Spiral Galaxy |journal=The Astrophysical Journal |date=2014 |volume=788 |issue=2 |page=174 |doi=10.1088/0004-637X/788/2/174 |arxiv=1404.6889 |bibcode=2014ApJ...788..174B }}</ref>

Black holes of any mass can have jets.<ref name="nemmen12">{{Cite journal |display-authors=2 |last1= Nemmen|first1= R. S.|last2= Georganopoulos|first2= M.|last3= Guiriec|first3= S.|last4= Meyer|first4= E. T.|last5= Gehrels|first5= N.|last6= Sambruna|first6= R. M.|title=A Universal Scaling for the Energetics of Relativistic Jets from Black Hole Systems|journal= Science|date= 2012|volume= 338|issue= 6113|pages= 1445–1448|doi= 10.1126/science.1227416|pmid= 23239730|arxiv= 1212.3343|bibcode= 2012Sci...338.1445N}}</ref> However, they are typically observed around spinning black holes with strongly-magnetized accretion disks.<ref name="bmr18" /><ref>{{Cite journal |display-authors=2 |last1=Chen 陈 |first1=Yongyun 永云 |last2=Gu 顾 |first2=Qiusheng 秋生 |last3=Fan 樊 |first3=Junhui 军辉 |last4=Zhou 周 |first4=Hongyan 宏岩 |last5=Yuan 袁 |first5=Yefei 业飞 |last6=Gu 顾 |first6=Weimin 为民 |last7=Wu 吴 |first7=Qinwen 庆文 |last8=Xiong 熊 |first8=Dingrong 定荣 |last9=Guo 郭 |first9=Xiaotong 晓通 |last10=Ding 丁 |first10=Nan 楠. |last11=Yu 俞 |first11=Xiaoling 效龄 |title=The Powers of Relativistic Jets Depend on the Spin of Accreting Supermassive Black Holes |journal=The Astrophysical Journal |date=2021 |volume=913 |issue=2 |page=93 |doi=10.3847/1538-4357/abf4ff |arxiv=2104.04242 |bibcode=2021ApJ...913...93C |doi-access=free }}</ref> Relativistic jets were more common in the [[Chronology of the universe#Gravity builds cosmic structure|early universe]], when galaxies and their corresponding supermassive black holes were rapidly gaining mass.<ref name="bmr18">{{Cite journal |last1=Blandford |first1=Roger |last2=Meier |first2=David |last3=Readhead |first3=Anthony |title=Relativistic Jets from Active Galactic Nuclei |journal=Annual Review of Astronomy and Astrophysics |date=2019 |volume=57 |pages=467–509 |doi=10.1146/annurev-astro-081817-051948 |arxiv=1812.06025 |bibcode=2019ARA&A..57..467B }}</ref><ref>{{Cite journal |display-authors=2 |last1=Ghisellini |first1=G. |last2=Haardt |first2=F. |last3=Ceca |first3=R. Della |last4=Volonteri |first4=M. |last5=Sbarrato |first5=T. |title=The Role of Relativistic Jets in the Heaviest and Most Active Supermassive Black Holes at High Redshift |journal=Monthly Notices of the Royal Astronomical Society |date=2013 |volume=432 |issue=4 |pages=2818–2823 |doi=10.1093/mnras/stt637 |doi-access=free }}</ref> All black holes with jets also have an accretion disk, but the jets are usually brighter than the disk.<ref name="mr99" /><ref>{{Cite journal |display-authors=2 |last1=Ghisellini |first1=G. |last2=Tavecchio |first2=F. |last3=Maraschi |first3=L. |last4=Celotti |first4=A. |last5=Sbarrato |first5=T. |title=The Power of Relativistic Jets Is Larger Than the Luminosity of Their Accretion Disks |journal=Nature |date=2014 |volume=515 |issue=7527 |pages=376–378 |doi=10.1038/nature13856 |pmid=25409827 |arxiv=1411.5368 |bibcode=2014Natur.515..376G }}</ref> ''[[Quasar]]s,'' typically found in other galaxies, are believed to be supermassive black holes with jets; ''[[microquasar]]s'' are believed to be stellar-mass objects with jets, typically observed in the Milky Way.<ref>{{Cite journal |last1=Mirabel |first1=I. F. |last2=Rodríguez |first2=L. F. |date=April 1998 |title=Microquasars in Our Galaxy |url=https://www.nature.com/articles/33603 |journal=Nature |language=en |volume=392 |issue=6677 |pages=673–676 |doi=10.1038/33603 |bibcode=1998Natur.392..673M |issn=0028-0836}}</ref>

The mechanism of formation of jets is not yet known,<ref name="nemmen12" /> but several options have been proposed. One method proposed to fuel these jets is the [[Blandford-Znajek process]], which suggests that the dragging of [[magnetic field lines]] by a black hole's rotation could launch jets of matter into space.<ref name="lwb00" /><ref>{{Cite journal |last1=Blandford |first1=R. D. |last2=Znajek |first2=R. L. |year=1977 |title=Electromagnetic Extraction of Energy from Kerr Black Holes |journal=[[Monthly Notices of the Royal Astronomical Society]] | volume=179 |issue=3 |page=433 |bibcode=1977MNRAS.179..433B |doi=10.1093/mnras/179.3.433 |doi-access=free |arxiv=astro-ph/0506302}}</ref> The [[Penrose process]], which involves extraction of a black hole's [[rotational energy]], has also been proposed as a potential mechanism of jet propulsion.<ref>{{cite journal |last1=Penrose |first1=R. |year=1969
|title=Gravitational Collapse: The Role of General Relativity |journal=[[Rivista del Nuovo Cimento]] | volume=1 |pages=252–276 |bibcode=1969NCimR...1..252P}}</ref><ref>{{Cite book |last1=Narayan |first1=Ramesh |last2=McClintock |first2=Jeffrey E. |last3=Tchekhovskoy |first3=Alexander |title=General Relativity, Cosmology and Astrophysics |chapter=Energy Extraction from Spinning Black Holes Via Relativistic Jets |date=2014 |pages=523–535 |doi=10.1007/978-3-319-06349-2_25 |arxiv=1303.3004 |isbn=978-3-319-06348-5 }}</ref>

==== Accretion disk ====
{{Main|Accretion disk}}

[[File:Black Hole Desktop & Phone Wallpapers (SVS14146 - BH accretion disk viz desktop).png|thumb|alt=An black hole with an orange-red accretion disk. The disk is wrapped around the black hole in a ring across its center and semicircles around the top and bottom of the black hole. The semicircles are actually the part of the accretion disk that is behind the black hole, and appears gravitationally lensed to be above and below the hole.|Visualization of a black hole with an orange accretion disk. The parts of the disk circling over and under the hole are actually gravitationally lensed from the back side of the black hole.<ref>{{Cite web |title=Black Hole Anatomy |url=https://science.nasa.gov/universe/black-holes/anatomy/ |archive-url=https://web.archive.org/web/20250424044622/https://science.nasa.gov/universe/black-holes/anatomy/ |archive-date=24 April 2025 |access-date=13 October 2025 |website=NASA Science |date=2 August 2022 }}</ref><ref>{{Cite journal |title=Lensing and Shadow of a Black Hole Surrounded by a Heavy Accretion Disk |journal=Journal of Cosmology and Astroparticle Physics |last1=Cunha |first1=Pedro |date=16 March 2020 |url=https://iopscience.iop.org/article/10.1088/1475-7516/2020/03/035 |volume=2020 |issue=3 |via=IOPscience |last2=Eiró |first2=Nelson |last3=Herdeiro |first3=Carlos |last4=Lemos |first4=José |page=035 |arxiv=1912.08833 |doi=10.1088/1475-7516/2020/03/035 |bibcode=2020JCAP...03..035C }}</ref>]]
Due to [[conservation of angular momentum]], gas falling into the [[gravitational well]] created by a massive object will typically form a disk-like structure around the object.<ref>{{Cite journal |last=Demtröder |first=Wolfgang |date=2024 |title=Astrophysics |url=https://link.springer.com/book/10.1007/978-3-031-22135-4 |journal=Undergraduate Lecture Notes in Physics |language=en |doi=10.1007/978-3-031-22135-4 |isbn=978-3-031-22133-0 |issn=2192-4791}}</ref>{{rp|242}} As the disk's angular momentum is transferred outward due to internal processes, its matter falls farther inward, converting its gravitational energy into heat and releasing a large amount of x-rays.<ref>{{Cite journal |last1=Blaes |first1=Omer |title=General Overview of Black Hole Accretion Theory |journal=Space Science Reviews |date=2014 |volume=183 |issue=1–4 |pages=21–41 |doi=10.1007/s11214-013-9985-6 |arxiv=1304.4879 |bibcode=2014SSRv..183...21B }}</ref><ref name="pt74">{{Cite journal |last1=Page |first1=Don N. |last2=Thorne |first2=Kip S. |title=Disk-Accretion Onto a Black Hole. Time-Averaged Structure of Accretion Disk |journal=The Astrophysical Journal |date=1974 |volume=191 |page=499 |doi=10.1086/152990 |bibcode=1974ApJ...191..499P }}</ref> The temperature of these disks can range from thousands to millions of [[kelvin]]s, and temperatures differ throughout a single accretion disk.<ref>{{Cite book |last1=Lasota |first1=Jean-Pierre |title=Astrophysics of Black Holes |chapter=Black Hole Accretion Discs |series=Astrophysics and Space Science Library |date=2016 |volume=440 |pages=1–60 |doi=10.1007/978-3-662-52859-4_1 |arxiv=1505.02172 |isbn=978-3-662-52857-0 }}</ref><ref>{{Cite journal |last1=Beloborodov |first1=A. M. |title=Super-Eddington Accretion Discs Around Kerr Black Holes |journal=Monthly Notices of the Royal Astronomical Society |date=1998 |volume=297 |issue=3 |pages=739–746 |doi=10.1046/j.1365-8711.1998.01530.x |arxiv=astro-ph/9802129 |bibcode=1998MNRAS.297..739B |doi-access=free }}</ref> Accretion disks can also emit in other parts of the [[electromagnetic spectrum]], depending on the disk's [[turbulence]] and [[magnetisation]] and the black hole's mass and angular momentum.<ref>{{multiref2|{{Cite journal |last1=Page |first1=Don N. |last2=Thorne |first2=Kip S. |title=Disk-Accretion Onto a Black Hole. Time-Averaged Structure of Accretion Disk |journal=The Astrophysical Journal |date=1974 |volume=191 |page=499 |doi=10.1086/152990 |bibcode=1974ApJ...191..499P }}|{{Cite journal |last1=Bisnovatyi-Kogan |first1=Gennady |title=Accretion into Black Hole, And Formation of Magnetically Arrested Accretion Disks |journal=Universe |date=2019 |volume=5 |issue=6 |page=146 |doi=10.3390/universe5060146 |arxiv=1905.13731 |bibcode=2019Univ....5..146B |doi-access=free }}|{{Cite journal |last1=Zakharov |first1=A. F. |last2=Repin |first2=S. V. |title=Model Radiation Spectrum for an Accretion Disk Near a Rotating Black Hole |journal=Astronomy Reports |date=2002 |volume=46 |issue=5 |pages=360–365 |doi=10.1134/1.1479423 |bibcode=2002ARep...46..360Z }}}}</ref>

Accretion disks can be defined as geometrically thin or geometrically thick. Geometrically thin disks are mostly confined to the black hole's equatorial plane and have a well-defined edge at the [[innermost stable circular orbit]] (ISCO), while geometrically thick disks are supported by internal pressure and temperature and can extend inside the ISCO. Disks with high rates of [[electron scattering]] and absorption, appearing bright and [[opaque]], are called ''optically thick''; ''optically thin'' disks are more [[translucent]] and produce fainter images when viewed from afar.<ref name="wang25">{{Cite journal |last1=Wang |first1=Zi-Liang |title=Exploring the Role of Accretion Disk Geometry in Shaping Black Hole Shadows |journal=Physical Review D |date=2025 |volume=112 |issue=6 |article-number=064052 |doi=10.1103/fhqj-wgcm |arxiv=2506.21148 |bibcode=2025PhRvD.112f4052W }}</ref> Accretion disks of black holes accreting beyond the [[Eddington limit]] are often referred to as ''polish donuts'' due to their thick, [[toroid]]al shape that resembles that of a [[donut]].<ref>{{Cite journal |last1=Gimeno-Soler |first1=Sergio |last2=Font |first2=José A. |title=Magnetised Polish Doughnuts Revisited |journal=Astronomy & Astrophysics |date=2017 |volume=607 |pages=A68 |doi=10.1051/0004-6361/201730935 |arxiv=1707.03867 |bibcode=2017A&A...607A..68G }}</ref><ref>{{Cite book |last1=Abramowicz |first1=M.A. |title=Growing Black Holes: Accretion in a Cosmological Context |chapter=Super-Eddington Black Hole Accretion |series=ESO Astrophysics Symposia |date=2005 |pages=257–273 |doi=10.1007/11403913_49 |isbn=978-3-540-25275-7 }}</ref>

Quasar accretion disks are expected to usually appear blue in colour.<ref>{{Cite journal |display-authors=2 |last1=Kishimoto |first1=Makoto |last2=Antonucci |first2=Robert |last3=Blaes |first3=Omer |last4=Lawrence |first4=Andy |last5=Boisson |first5=Catherine |last6=Albrecht |first6=Marcus |last7=Leipski |first7=Christian |title=The Characteristic Blue Spectra of Accretion Disks in Quasars as Uncovered in the Infrared |journal=Nature |date=2008 |volume=454 |issue=7203 |pages=492–494 |doi=10.1038/nature07114 |pmid=18650919 |arxiv=0807.3703 |bibcode=2008Natur.454..492K }}</ref> The disk for a stellar black hole, on the other hand, would likely look orange, yellow, or red, with its inner regions being the brightest.<ref>{{Cite journal |last1=Fukue |first1=Jun |last2=Yokoyama |first2=Takushi |title=Color Photographs of an Accretion Disk Around a Black Hole |journal=Publications of the Astronomical Society of Japan |date=1988 |volume=40 |pages=15–24 |doi=10.1093/pasj/40.1.15}}</ref> Theoretical research suggests that the hotter a disk is, the bluer it should be, although this is not always supported by observations of real astronomical objects.<ref>{{Cite journal |display-authors=2 |last1=Bonning |first1=E. W. |last2=Cheng |first2=L. |last3=Shields |first3=G. A. |last4=Salviander |first4=S. |last5=Gebhardt |first5=K. |title=Accretion Disk Temperatures and Continuum Colors in QSOs |journal=The Astrophysical Journal |date=2007 |volume=659 |issue=1 |pages=211–217 |doi=10.1086/510712 |arxiv=astro-ph/0611263 |bibcode=2007ApJ...659..211B }}</ref> Accretion disk colours may also be altered by the [[Doppler effect]], with the part of the disk travelling towards an observer appearing bluer and brighter and the part of the disk travelling away from the observer appearing redder and dimmer.<ref name="jtft15">{{Cite journal |display-authors=2 |last1=James |first1=Oliver |last2=Tunzelmann |first2=Eugénie von |last3=Franklin |first3=Paul |last4=Thorne |first4=Kip S. |title=Gravitational Lensing by Spinning Black Holes in Astrophysics, And in the Movie ''Interstellar'' |journal=Classical and Quantum Gravity |date=2015 |volume=32 |issue=6 |doi=10.1088/0264-9381/32/6/065001 |arxiv=1502.03808 |bibcode=2015CQGra..32f5001J }}</ref><ref>{{Cite journal |display-authors=2 |last1=Guo |first1=Sen |last2=Huang |first2=Yu-Xiang |last3=Cui |first3=Yu-Hao |last4=Han |first4=Yan |last5=Jiang |first5=Qing-Quan |last6=Liang |first6=En-Wei |last7=Lin |first7=Kai |title=Unveiling the Unconventional Optical Signatures of Regular Black Holes Within Accretion Disk |journal=The European Physical Journal C |date=2023 |volume=83 |issue=11 |article-number=1059 |doi=10.1140/epjc/s10052-023-12208-0  |doi-access=free|arxiv=2310.20523 |bibcode=2023EPJC...83.1059G }}</ref>

==== Innermost stable circular orbit (ISCO) ====
{{Main|Innermost stable circular orbit}}

[[File:How to Measure the Spin of a Black Hole.jpg|thumb|alt=Artistic depiction of three black holes, showing that the accretion disk is closer to the black hole if it is orbiting in the same direction that the black hole is rotating. Graphs next to these images show changes in the x-ray spectra released by the disks.|Since particles in a black hole's accretion disk must orbit at or outside the ISCO, astronomers can observe the properties of accretion disks to determine black hole spins.<ref>{{Cite journal |display-authors=2 |last1=McClintock |first1=Jeffrey E. |last2=Narayan |first2=Ramesh |last3=Davis |first3=Shane W. |last4=Gou |first4=Lijun |last5=Kulkarni |first5=Akshay |last6=Orosz |first6=Jerome A. |last7=Penna |first7=Robert F. |last8=Remillard |first8=Ronald A. |last9=Steiner |first9=James F. |title=Measuring the Spins of Accreting Black Holes |journal=Classical and Quantum Gravity |date=2011 |volume=28 |issue=11 |doi=10.1088/0264-9381/28/11/114009 |arxiv=1101.0811 |bibcode=2011CQGra..28k4009M }}</ref>]]
In [[Newton's law of universal gravitation|Newtonian gravity]], [[test particle]]s can stably orbit at arbitrary distances from a central object. In general relativity, however, there exists a smallest possible radius for which a massive particle can orbit stably. Any infinitesimal inward [[perturbation (astronomy)|perturbations]] to this orbit will lead to the particle [[orbital decay|spiraling into]] the black hole, and any outward perturbations will, depending on the energy, cause the particle to spiral in, move to a stable orbit further from the black hole, or escape to infinity. This orbit is called the '''innermost stable circular orbit''', or ISCO.<ref name="Misner-1973">{{cite book |last1=Misner |first1=Charles |last2=Thorne |first2=Kip S. |last3=Wheeler |first3=John |author1-link=Charles W. Misner |author2-link=Kip Thorne |author3-link=John Archibald Wheeler |title=Gravitation |publisher=W. H. Freeman and Company |date=1973 |isbn=978-0-7167-0344-0}}</ref><ref name="jtb15">{{Cite journal |last1=Jefremov |first1=Paul I. |last2=Tsupko |first2=Oleg Yu. |last3=Bisnovatyi-Kogan |first3=Gennady S. |title=Innermost Stable Circular Orbits of Spinning Test Particles in Schwarzschild and Kerr Space-Times |journal=Physical Review D |date=2015 |volume=91 |issue=12 |article-number=124030 |doi=10.1103/PhysRevD.91.124030 |arxiv=1503.07060 |bibcode=2015PhRvD..91l4030J }}</ref> The location of the ISCO depends on the spin of the black hole and the [[spin (physics)|spin]] of the particle itself. In the case of a Schwarzschild black hole (spin zero) and a particle without spin, the location of the ISCO is:
<math display="block">r_{\rm ISCO}=3 \, r_\text{s}=\frac{6 \, GM}{c^2},</math> where <math>r_{\rm_{ISCO}}</math> is the radius of the ISCO, <math>r_\text{s}</math> is the Schwarzschild radius of the black hole, <math>G</math> is the gravitational constant, and <math>c</math> is the speed of light.<ref name="Bardeen1972" />
The radius of this orbit changes slightly based on particle spin.<ref name="zwgsl18">{{Cite journal |display-authors=2 |last1=Zhang |first1=Yu-Peng |last2=Wei |first2=Shao-Wen |last3=Guo |first3=Wen-Di |last4=Sui |first4=Tao-Tao |last5=Liu |first5=Yu-Xiao |title=Innermost Stable Circular Orbit of Spinning Particle in Charged Spinning Black Hole Background |journal=Physical Review D |date=2018 |volume=97 |issue=8 |article-number=084056 |doi=10.1103/PhysRevD.97.084056 |arxiv=1711.09361 |bibcode=2018PhRvD..97h4056Z }}</ref><ref>{{Cite journal |last1=Tsupko |first1=O. Yu. |last2=Bisnovatyi-Kogan |first2=G. S. |last3=Jefremov |first3=P. I. |title=Parameters of Innermost Stable Circular Orbits of Spinning Test Particles: Numerical and Analytical Calculations |journal=Gravitation and Cosmology |date=2016 |volume=22 |issue=2 |pages=138–147 |doi=10.1134/S0202289316020158 |arxiv=1605.04189 |bibcode=2016GrCo...22..138T }}</ref> For charged black holes, the ISCO moves inwards.<ref name="zwgsl18" /> For spinning black holes, the ISCO is moved inwards for particles orbiting in the same direction that the black hole is spinning ([[retrograde and prograde motion|prograde]]) and outwards for particles orbiting in the opposite direction (retrograde).<ref name="jtb15" /> For example, the ISCO for a particle orbiting retrograde can be as far out as about <math>4.5r_\text{s}</math>, while the ISCO for a particle orbiting prograde can be as close as at the event horizon itself.<ref name="jtb15" /><ref>{{Cite book |last1=Jefremov |first1=Paul I. |last2=Tsupko |first2=Oleg Yu. |last3=Bisnovatyi-Kogan |first3=Gennady S. |title=The Fourteenth Marcel Grossmann Meeting |chapter=Spin-induced changes in the parameters of ISCO in Kerr spacetime |date=2017 |pages=3715–3721 |doi=10.1142/9789813226609_0486 |isbn=978-981-322-659-3 }}</ref>

==== Photon sphere and shadow ====
{{anchor|Photon sphere}}
{{Main|Photon sphere}}

[[File:Photon capture by a Schwarzschild black hole - video.ogg|thumb|thumbtime=6|Video of a photon being captured by a Schwarzschild black hole |alt=A photon (small, black with yellow trail) being captured in the [[photon sphere]] of a Schwarzschild black hole (large, black, center)]]

The [[photon sphere]] is a spherical boundary for which photons moving on tangents to that sphere are bent completely around the black hole, possibly orbiting multiple times.<ref>{{Cite journal |last1=Vázquez |first1=S.E. |last2=Esteban |first2=E.P. |date=December 7, 2004 |title=Strong-Field Gravitational Lensing by a Kerr Black Hole |url=https://doi.org/10.1393/ncb/i2004-10121-y |journal=Il Nuovo Cimento B |volume=119 |issue=5 |pages=489–519 |doi=10.1393/ncb/i2004-10121-y |arxiv=gr-qc/0308023 |bibcode=2004NCimB.119..489V }}</ref> For Schwarzschild black holes, the photon sphere has a radius 1.5 times the Schwarzschild radius.<ref name="ll19">{{Cite journal |last1=Lü |first1=H. |last2=Lyu |first2=Hong-Da |title=Schwarzschild Black Holes Have the Largest Size |journal=Physical Review D |date=2020 |volume=101 |issue=4 |article-number=044059 |doi=10.1103/PhysRevD.101.044059 |arxiv=1911.02019 |bibcode=2020PhRvD.101d4059L }}</ref><ref name="qiao22">{{Cite journal |last1=Qiao |first1=Chen-Kai |title=Curvatures, Photon Spheres, And Black Hole Shadows |journal=Physical Review D |date=2022 |volume=106 |issue=8 |article-number=084060 |doi=10.1103/PhysRevD.106.084060 |arxiv=2208.01771 |bibcode=2022PhRvD.106h4060Q }}</ref> When viewed from a great distance, the photon sphere creates an observable '''black hole shadow'''.{{anchor|Black hole shadow}}<ref name="ll19" /> Since no light emerges from within the black hole, this shadow is the limit for possible observations.<ref>{{Cite journal |last=Horvath |first=Jorge Ernesto |date=2022 |title=High-Energy Astrophysics |url=https://link.springer.com/book/10.1007/978-3-030-92159-0 |journal=Undergraduate Lecture Notes in Physics |language=en |doi=10.1007/978-3-030-92159-0 |isbn=978-3-030-92158-3 |issn=2192-4791}}</ref>{{rp|152}} The shadow of colliding black holes should have characteristic warped shapes, allowing scientists to detect black holes that are about to merge.<ref name="prd84_6">{{cite journal |last1=Nitta |first1=Daisuke |last2=Chiba |first2=Takeshi |last3=Sugiyama |first3=Naoshi |title=Shadows of Colliding Black Holes |journal=Physical Review D |volume=84 |issue=6 |article-number=063008 |date=September 2011 |doi=10.1103/PhysRevD.84.063008 |bibcode=2011PhRvD..84f3008N |arxiv=1106.2425 |s2cid=119264596}}</ref>

While light can still escape from the photon sphere, any light that crosses the photon sphere on an inbound trajectory will be captured by the black hole. Therefore, any light that reaches an outside observer from the photon sphere must have been emitted by objects between the photon sphere and the event horizon.<ref name="prd84_6" /> Light emitted towards the photon sphere may also curve around the black hole and return to the emitter.<ref>{{Cite journal |last=Cramer |first=Claes R. |date=April 1997 |title=Using the Uncharged Kerr Black Hole as a Gravitational Mirror |url=https://link.springer.com/10.1023/A:1018878515046 |journal=General Relativity and Gravitation |language=en |volume=29 |issue=4 |pages=445–454 |doi=10.1023/A:1018878515046 |arxiv=gr-qc/9510053 |bibcode=1997GReGr..29..445C |issn=0001-7701}}</ref>

For a rotating, uncharged black hole, the radius of the photon sphere depends on the spin parameter and whether the photon is orbiting prograde or retrograde.<ref name="Bardeen1972">{{cite journal|last1=Bardeen|first1=James M.|last2=Press|first2=William H.|last3=Teukolsky|first3=Saul A.|date=1 December 1972|title=Rotating Black Holes: Locally Nonrotating Frames, Energy Extraction, And Scalar Synchrotron Radiation|journal=The Astrophysical Journal|volume=178|pages=347–370|doi=10.1086/151796|bibcode=1972ApJ...178..347B}}</ref> For a photon orbiting prograde, the photon sphere will be 0.5-1.5 Schwarzschild radii from the center of the black hole, while for a photon orbiting retrograde, the photon sphere will be between 3-4 Schwarzschild radii from the center of the black hole. The exact locations of the photon spheres depend on the [[magnitude (mathematics)#numbers|magnitude]] of the black hole's rotation.<ref>{{Cite journal |last1=Teo |first1=Edward |title=Spherical Photon Orbits Around a Kerr Black Hole |journal=General Relativity and Gravitation |date=2003 |volume=35 |issue=11 |pages=1909–1926 |doi=10.1023/A:1026286607562 |bibcode=2003GReGr..35.1909T |url=http://scholarbank.nus.edu.sg/handle/10635/97985 }}</ref> For a charged, nonrotating black hole, there will only be one photon sphere, and the radius of the photon sphere will decrease for increasing black hole charge.<ref>{{Cite journal |last1=Heydarzade |first1=Yaghoub |last2=Vertogradov |first2=Vitalii |title=Dynamical Photon Spheres in Charged Black Holes and Naked Singularities |journal=The European Physical Journal C |date=2024 |volume=84 |issue=6 |article-number=582 |doi=10.1140/epjc/s10052-024-12945-w  |doi-access=free|arxiv=2311.08930 |bibcode=2024EPJC...84..582H }}</ref> For non-[[extremal black hole|extremal]], charged, rotating black holes, there will always be two photon spheres, with the exact radii depending on the parameters of the black hole.<ref>{{Cite journal |last1=Chen |first1=Ying-Xuan |last2=Huang |first2=Jia-Hui |last3=Jiang |first3=Haoxiang |title=Radii of Spherical Photon Orbits Around Kerr-Newman Black Holes |journal=Physical Review D |date=2023 |volume=107 |issue=4 |article-number=044066 |doi=10.1103/PhysRevD.107.044066 |arxiv=2210.08509 |bibcode=2023PhRvD.107d4066C }}</ref>

==== Ergosphere ====
{{Main|Ergosphere}}

[[File:Ergosphere and event horizon of a rotating black hole (no animation).gif|thumb|alt=The ergosphere as a peanut-shaped region that touches the event horizon in the middle and then bulges outwards at the poles. The black hole depicted has a spin 99% of the maximum.|The ergosphere is a region outside of the event horizon, where objects cannot remain in place.<ref name="viss">{{cite arXiv |eprint=0706.0622 |last1=Visser |first1=Matt |title=The Kerr Spacetime: A Brief Introduction |class=gr-qc |year=2007 |at=page 35, Fig. 3}}</ref>]]

Near a rotating black hole, spacetime rotates similar to a vortex. The rotating spacetime will drag any matter and light into rotation around the spinning black hole. This effect of general relativity, called [[frame dragging]], gets stronger closer to the spinning mass. The region of spacetime in which it is impossible to stay still is called the ergosphere.<ref name="reynolds18">{{Cite journal |last1=Reynolds |first1=Christopher S. |title=Observing Black Holes Spin |journal=Nature Astronomy |date=2019 |volume=3 |pages=41–47 |doi=10.1038/s41550-018-0665-z |arxiv=1903.11704 |bibcode=2019NatAs...3...41R }}</ref>

The ergosphere of a black hole is a volume bounded by the black hole's event horizon and the ''ergosurface'', which coincides with the event horizon at the poles but bulges out from it around the equator.<ref name="viss" />

Matter and radiation can escape from the ergosphere. Through the [[Penrose process]], objects can emerge from the ergosphere with more energy than they entered with. The extra energy is taken from the rotational energy of the black hole, slowing down the rotation of the black hole.<ref name="Carroll-2019">{{Cite book |last=Carroll |first=Sean M. |url=https://www.cambridge.org/core/product/identifier/9781108770385/type/book |title=Spacetime and Geometry: An Introduction to General Relativity |date=August 8, 2019 |publisher=Cambridge University Press |isbn=978-1-108-48839-6 |edition=1 |doi=10.1017/9781108770385}}</ref>{{rp|268}} A variation of the Penrose process in the presence of strong magnetic fields, the [[Blandford–Znajek process]], is considered a likely mechanism for the enormous luminosity and relativistic jets of [[quasars]] and other [[active galactic nuclei]].<ref name="lwb00">{{Cite journal |last1=Lee |first1=Hyun Kyu |last2=Wijers |first2=R.A.M.J. |last3=Brown |first3=G.E. |title=The Blandford–Znajek Process as a Central Engine for a Gamma-Ray Burst |journal=Physics Reports |date=2000 |volume=325 |issue=3 |pages=83–114 |doi=10.1016/S0370-1573(99)00084-8 |arxiv=astro-ph/9906213 |bibcode=2000PhR...325...83L }}</ref><ref>{{cite news|url=https://phys.org/news/2018-02-dynamics-black-hole-rotational-energy.html|title=Researchers Clarify Dynamics of Black Hole Rotational Energy|access-date=17 September 2018|archive-date=17 September 2018|archive-url=https://web.archive.org/web/20180917105330/https://phys.org/news/2018-02-dynamics-black-hole-rotational-energy.html|url-status=live}}</ref>

==== Plunging region ====
{{Main|Plunging region}}

The observable region of spacetime around a black hole closest to its event horizon is called the plunging region. In this area it is no longer possible for free falling matter to follow circular orbits or stop a final descent into the black hole. Instead, it will rapidly plunge toward the black hole at close to the speed of light, growing increasingly hot and producing a characteristic, detectable [[thermal radiation|thermal emission]].<ref>{{cite journal |display-authors=2 |last1=Mummery |first1=Andrew |last2=Ingram |first2=Adam |last3=Davis |first3=Shane |last4=Fabian |first4=Andrew |title=Continuum Emission from Within the Plunging Region of Black Hole Discs |journal=Monthly Notices of the Royal Astronomical Society |volume=531 |issue=1 |pages=366–386 |date=June 2024 |doi=10.1093/mnras/stae1160|doi-access=free |arxiv=2405.09175 }}</ref><ref>{{Cite journal |last1=Machida |first1=Mami |last2=Matsumoto |first2=Ryoji |title=Global Three-Dimensional Magnetohydrodynamic Simulations of Black Hole Accretion Disks: X-Ray Flares in the Plunging Region |journal=The Astrophysical Journal |date=2003 |volume=585 |issue=1 |pages=429–442 |doi=10.1086/346070 |arxiv=astro-ph/0211240 |bibcode=2003ApJ...585..429M }}</ref> However, light and radiation emitted from this region can still escape from the black hole's gravitational pull.<ref name="prisco">{{Cite web |title=Study Proves Black Holes Have a 'Plunging Region,' Just as Einstein Predicted |url=https://www.cnn.com/2024/05/17/world/black-holes-einstein-plunging-region-scn |last=Prisco |first=Jacopo |website=[[CNN]] | date=17 May 2024}}</ref>

=== Radius ===
For a nonspinning, uncharged black hole, the radius of the event horizon, or Schwarzschild radius, is proportional to the mass, ''M'', through
<math display="block">r_\mathrm{s}=\frac{2GM}{c^2} \approx 2.95\, \frac{M}{M_\odot}~\mathrm{km,}</math>
where ''r''{{sub|s}} is the Schwarzschild radius, ''G'' is the [[gravitational constant]], ''c'' is the [[speed of light]], and {{solar mass}} is the [[solar mass|mass of the Sun]].<ref>{{cite book |last=Wald |first=Robert M. |author-link=Robert Wald |title=General Relativity |publisher=University of Chicago Press |date=1984 |isbn=978-0-226-87033-5 |url=https://books.google.com/books?id=9S-hzg6-moYC |access-date=23 February 2016 |archive-date=11 August 2016 |archive-url=https://web.archive.org/web/20160811035125/https://books.google.com/books?id=9S-hzg6-moYC |url-status=live }}</ref>{{rp|124}} For a black hole of the same mass with nonzero spin or electric charge, the radius is smaller.{{refn|group=Note|The (outer) event horizon radius scales as: <math>M + \sqrt{M^2 - {{(J/M)}}^2 - Q^2}.</math>}} As a black hole's charge and spin approach the maximum allowed value, the radius of the event horizon nears
<math display="block">r_\mathrm{+}=\frac{GM}{c^2},</math>
half the radius of a nonspinning, uncharged black hole of the same mass.<ref>{{cite journal |last1=Saa |first1=Alberto |last2=Santarelli |first2=Raphael |title=Destroying a Near-Extremal Kerr–Newman Black Hole |journal=Physical Review D |date=18 July 2011 |volume=84 |issue=2 |article-number=027501 |doi=10.1103/PhysRevD.84.027501 |arxiv=1105.3950 |bibcode=2011PhRvD..84b7501S|s2cid=118487989 }}</ref>

Since the volume within the Schwarzschild radius increases with the cube of the radius, average density of a black hole inside its Schwarzschild radius is inversely proportional to the square of its mass: supermassive black holes are much less dense than stellar black holes. The average density of a {{Solar mass|{{10^|8}}}} black hole is comparable to that of water.<ref name="CMS1999" /><ref>{{Cite journal |last1=Reid |first1=M. J. |last2=Brunthaler |first2=A. |title=The Proper Motion of Sagittarius A*. III. The Case for a Supermassive Black Hole |journal=The Astrophysical Journal |date=2020 |volume=892 |issue=1 |page=39 |doi=10.3847/1538-4357/ab76cd |arxiv=2001.04386 |bibcode=2020ApJ...892...39R |doi-access=free }}</ref>

=== Event horizon ===
{{Main|Event horizon}}

{{multiple image
| align             = right
| direction         = vertical
| width             = 300
| image1            = BH-no-escape-1.svg
| alt1              = A light cone near the event horizon of a black hole with arrows coming out of it to show the directions that a particle there can move. It is far enough away from the event horizon that that it is not warped towards the event horizon and a particle there can move in any direction.
| caption1          = Far away from the black hole, a particle can move in any direction, as illustrated by the set of arrows. It is restricted only by the speed of light.
| image2            = BH-no-escape-2.svg
| alt2              = A light cone very close to the event horizon of a black hole, with arrows coming out of it to show the directions that a particle there can move. It is bent towards the event horizon, with more arrows going towards the event horizon than away, but a particle can still travel away from the event horizon.
| caption2          = Closer to the black hole, spacetime starts to deform. There are more paths going towards the black hole than paths moving away.{{refn|The set of possible paths, or more accurately the future [[light cone]] containing all possible [[world line]]s (in this diagram the light cone is represented by the V-shaped region bounded by arrows representing light ray world lines), is tilted in this way in [[Eddington–Finkelstein coordinates]] (the diagram is a "cartoon" version of an Eddington–Finkelstein coordinate diagram), but in other coordinates the light cones are not tilted in this way, for example in [[Schwarzschild coordinates]] they narrow without tilting as one approaches the event horizon, and in [[Kruskal–Szekeres coordinates]] the light cones do not change shape or orientation at all.<ref name="Misner-1973" />{{rp|p=848}}|group="Note"}}
| image3            = BH-no-escape-3.svg
| caption3          = Inside of the event horizon, all paths bring the particle closer to the centre of the black hole. It is no longer possible for the particle to escape.
| alt3              = A light cone inside of the event horizon of a black hole, with arrows coming out of it to show the directions that a particle there can move. All of the arrows lead further inside the event horizon, with none leading outwards.
}}

The defining feature of a black hole is the existence of an event horizon, a boundary in [[spacetime]] through which matter and light can pass only inward towards the center of the black hole. Nothing, not even light, can escape from inside the event horizon.<ref>{{cite book |title=The New Physics |edition=illustrated |first1=Paul |last1=Davies |publisher=Cambridge University Press |year=1992 |isbn=978-0-521-43831-5 |page=26 |url=https://books.google.com/books?id=akb2FpZSGnMC |access-date=25 September 2020 |archive-date=17 August 2021 |archive-url=https://web.archive.org/web/20210817161727/https://books.google.com/books?id=akb2FpZSGnMC |url-status=live }} [https://books.google.com/books?id=akb2FpZSGnMC&pg=PA26 Extract of page 26] {{Webarchive|url=https://web.archive.org/web/20210815222341/https://books.google.com/books?id=akb2FpZSGnMC&pg=PA26 |date=15 August 2021 }}</ref><ref>{{cite book |title=A Student's Guide to the Mathematics of Astronomy |edition=illustrated |first1=Daniel |last1=Fleisch |first2=Julia |last2=Kregenow |publisher=Cambridge University Press |year=2013 |isbn=978-1-107-03494-5 |page=168 |url=https://books.google.com/books?id=x4gaBQAAQBAJ |access-date=25 September 2020 |archive-date=17 August 2021 |archive-url=https://web.archive.org/web/20210817045139/https://books.google.com/books?id=x4gaBQAAQBAJ |url-status=live }} [https://books.google.com/books?id=x4gaBQAAQBAJ&pg=PA168 Extract of page 168] {{Webarchive|url=https://web.archive.org/web/20210817113029/https://books.google.be/books?id=x4gaBQAAQBAJ&pg=PA168 |date=17 August 2021 }}</ref> The event horizon is referred to as such because if an event occurs within the boundary, information from that event cannot reach or affect an outside observer, making it impossible to determine whether such an event occurred.<ref name="JCWheeler-2007" />{{rp|179}}
For non-rotating black holes, the geometry of the event horizon is precisely spherical, while for rotating black holes, the event horizon is [[oblate spheroid|oblate]].<ref name="Smarr1973">{{cite journal|last1= Smarr|first1= L.|title=Surface Geometry of Charged Rotating Black Holes |journal= Physical Review D|volume= 7|issue= 2|year= 1973|pages= 289–295|doi= 10.1103/PhysRevD.7.289|bibcode= 1973PhRvD...7..289S}}</ref><ref name="Wiltshire2009">{{cite book|author= Visser, M.|editor1= Wiltshire, D.L.|editor2= Visser, M.|editor3= Scott, S.M.|title=Horizon Geometry for Kerr Black Holes with Synchronized Hair|url= https://books.google.com/books?id=wymJBq_80Q0C|chapter= The Kerr spacetime: A brief introduction|date= 22 January 2009|volume= 97|issue= 12|article-number= 124012|publisher= Cambridge University Press|doi= 10.1103/PhysRevD.97.124012|isbn= 978-0-521-88512-6|arxiv= 0706.0622|bibcode= 2018PhRvD..97l4012D|access-date= 12 January 2020|archive-date= 20 May 2020|archive-url= https://web.archive.org/web/20200520134643/https://books.google.com/books?id=wymJBq_80Q0C|url-status= live}}</ref>

To a distant observer, a clock near a black hole would appear to tick more slowly than one further from the black hole.<ref name="Carroll-2004" />{{rp|p=217}}<ref name="scienceofinterstellar" /> This effect, known as [[gravitational time dilation]], would also cause an object falling into a black hole to appear to slow as it approached the event horizon, never quite reaching the horizon from the perspective of an outside observer.<ref name="Carroll-2004" />{{rp|p=218}} All processes on this object would appear to slow down, and any light emitted by the object to appear redder and dimmer, an effect known as [[gravitational redshift]].<ref>{{cite web |url=http://nrumiano.free.fr/Estars/int_bh.html |title=Inside a Black Hole |website=Knowing the universe and its secrets |access-date=26 March 2009 |archive-url=https://web.archive.org/web/20090423053437/http://nrumiano.free.fr/Estars/int_bh.html |archive-date=23 April 2009 }}</ref> An object falling from half of a Schwarzschild radius above the event horizon would fade away until it could no longer be seen, disappearing from view within one hundredth of a second.<ref>{{cite web |title=What Happens to You If You Fall into a Black Hole |url=http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html |website=math.ucr.edu |publisher=[[John Baez]] | access-date=11 March 2018 |archive-date=13 February 2019 |archive-url=https://web.archive.org/web/20190213124648/http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html |url-status=live }}</ref> It would also appear to flatten onto the black hole, joining all other material that had ever fallen into the hole.<ref>{{Cite magazine |date=1997-04-01 |title=Black Holes and the Information Paradox |magazine=Scientific American |last=Susskind |first=Leonard |url=https://www.jstor.org/stable/24993702?seq=1 |access-date=2025-12-09 |page=52-57 |issue=April 1997 |author-link=Leonard Susskind |jstor=24993702 }}</ref>

On the other hand, an observer falling into a black hole would not notice any of these effects as they cross the event horizon. Their own clocks appear to them to tick normally, and they cross the event horizon after a finite time without noting any singular behaviour. In [[general relativity]], it is impossible to determine the location of the event horizon from local observations, due to Einstein's [[equivalence principle]].<ref name="Carroll-2004" />{{rp|p=222}}<ref name="HamiltonA">{{cite web|author=Hamilton, A.|url=http://jila.colorado.edu/~ajsh/insidebh/schw.html|title=Journey into a Schwarzschild black hole|website=jila.colorado.edu|access-date=28 June 2020|archive-date=3 September 2019|archive-url=https://web.archive.org/web/20190903235853/https://jila.colorado.edu/~ajsh/insidebh/schw.html|url-status=live}}</ref>

=== Internal geometry ===
==== Cauchy horizon ====
{{Main|Cauchy horizon}}

Black holes that are rotating and/or charged have an inner horizon, often called the Cauchy horizon, inside of the black hole.<ref name="pi90">{{Cite journal |last1=Poisson |first1=Eric |last2=Israel |first2=Werner |title=Internal Structure of Black Holes |journal=Physical Review D |date=1990 |volume=41 |issue=6 |pages=1796–1809 |doi=10.1103/PhysRevD.41.1796 |pmid=10012548 |bibcode=1990PhRvD..41.1796P }}</ref> The inner horizon is divided up into two segments: an ingoing section and an outgoing section.<ref name="st14">{{Cite journal |last1=Scheel |first1=M. A. |last2=Thorne |first2=K. S. |title=Geometrodynamics: The Nonlinear Dynamics of Curved Spacetime |journal=Physics-Uspekhi |date=2014 |volume=57 |issue=4 |pages=342–351 |doi=10.3367/UFNe.0184.201404b.0367 |arxiv=1706.09078 |bibcode=2014PhyU...57..342S }}</ref>

At the ingoing section of the Cauchy horizon, radiation and matter that fall into the black hole would build up at the horizon, causing the curvature of spacetime to go to infinity. This would cause an observer falling in to experience tidal forces.<ref name="pi90" /><ref name="st14" /> This phenomenon is often called [[mass inflation]], since it is associated with a [[parameter]] dictating the black hole's internal mass [[exponential growth|growing exponentially]],<ref name="pi90" /><ref name="mo12">{{Cite journal |last1=Marolf |first1=Donald |last2=Ori |first2=Amos |title=Outgoing Gravitational Shock Wave at the Inner Horizon: The Late-Time Limit of Black Hole Interiors |journal=Physical Review D |date=2012 |volume=86 |issue=12 |article-number=124026 |doi=10.1103/PhysRevD.86.124026 |arxiv=1109.5139 |bibcode=2012PhRvD..86l4026M }}</ref> and the buildup of tidal forces is called the mass-inflation singularity<ref name="ori91">{{Cite journal |last1=Ori |first1=Amos |title=Inner Structure of a Charged Black Hole: An Exact Mass-Inflation Solution |journal=Physical Review Letters |date=1991 |volume=67 |issue=7 |pages=789–792 |doi=10.1103/PhysRevLett.67.789 |pmid=10044989 |bibcode=1991PhRvL..67..789O }}</ref><ref name="st14" /> or Cauchy horizon singularity.<ref>{{Cite journal |last1=Burko |first1=Lior M. |title=Structure of the Black Hole's Cauchy-Horizon Singularity |journal=Physical Review Letters |date=1997 |volume=79 |issue=25 |pages=4958–4961 |doi=10.1103/PhysRevLett.79.4958 |arxiv=gr-qc/9710112 |bibcode=1997PhRvL..79.4958B }}</ref><ref>{{Cite journal |last1=Burko |first1=Lior M. |last2=Khanna |first2=Gaurav |last3=Zenginoǧlu |first3=Anıl |title=Cauchy-Horizon Singularity Inside Perturbed Kerr Black Holes |journal=Physical Review D |date=2016 |volume=93 |issue=4 |article-number=041501 |doi=10.1103/PhysRevD.93.041501 |arxiv=1601.05120 |bibcode=2016PhRvD..93d1501B }}</ref> Some physicists have argued that in realistic black holes, accretion and Hawking radiation would stop mass inflation from occurring.<ref>{{Cite journal |last1=Hamilton |first1=Andrew J. S. |title=Mass Inflation Followed by Belinskii-Khalatnikov-Lifshitz Collapse Inside Accreting, Rotating Black Holes |journal=Physical Review D |date=2017 |volume=96 |issue=8 |article-number=084041 |doi=10.1103/PhysRevD.96.084041 |arxiv=1703.01921 |bibcode=2017PhRvD..96h4041H }}</ref><ref>{{Cite journal |display-authors=2 |last1=Barceló |first1=Carlos |last2=Boyanov |first2=Valentin |last3=Carballo-Rubio |first3=Raúl |last4=Garay |first4=Luis J. |title=Classical Mass Inflation Versus Semiclassical Inner Horizon Inflation |journal=Physical Review D |date=2022 |volume=106 |issue=12 |article-number=124006 |doi=10.1103/PhysRevD.106.124006 |arxiv=2203.13539 |bibcode=2022PhRvD.106l4006B }}</ref>

At the outgoing section of the inner horizon, infalling radiation would [[backscatter]] off of the black hole's spacetime curvature and travel outward, building up at the outgoing Cauchy horizon. This would cause an infalling observer to experience a gravitational [[shock wave]] and tidal forces as the spacetime curvature at the horizon grew to infinity. This buildup of tidal forces is called the [[shock singularity]].<ref name="mo12" /><ref name="st14" />

Both of these singularities are [[Penrose-Hawking singularity theorems#Singularities|weak]], meaning that an object crossing them would only be deformed a finite amount by tidal forces, even though the spacetime curvature would still be infinite at the singularity. This is as opposed to a [[Penrose-Hawking singularity theorems#Singularities|strong singularity]], where an object hitting the singularity would be stretched and squeezed by an infinite amount.<ref name="ori91" /><ref name="mo12" /> They are also [[Penrose-Hawking singularity theorems#Singularities|null singularities]], meaning that a photon could travel [[parallel (geometry)|parallel]] to them without ever being intercepted.<ref name="st14" />

==== Singularity ====
{{Main|Gravitational singularity}}

Ignoring quantum effects, every black hole has a singularity inside, points where the curvature of spacetime becomes infinite, and [[geodesic]]s terminate within a finite [[proper time]].<ref name="Carroll-2004" />{{rp|p=205}}<ref name="hp70">{{Cite journal |last1=Hawking |first1=S. W. |last2=Penrose |first2=R. |title=The Singularities of Gravitational Collapse and Cosmology |journal=Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences |date=1970 |volume=314 |issue=1519 |pages=529–548 |doi=10.1098/rspa.1970.0021 |bibcode=1970RSPSA.314..529H }}</ref> For a non-rotating black hole, this region takes the shape of a single point; for a rotating black hole it is smeared out to form a [[ring singularity]] that lies in the plane of rotation.<ref name="Carroll-2004" />{{rp|p=264}} In both cases, the singular region has zero volume. All of the mass of the black hole ends up in the singularity.<ref name="Carroll-2004" />{{rp|p=252}} Since the singularity has nonzero mass in an infinitely small space, it can be thought of as having infinite [[mass density|density]].<ref>{{cite news |title=Sizes of Black Holes? How Big Is a Black Hole? |url=https://www.skyandtelescope.com/astronomy-resources/how-big-is-a-black-hole/ |access-date=9 October 2018 |work=[[Sky & Telescope]] | date=22 July 2014 |archive-date=3 April 2019 |archive-url=https://web.archive.org/web/20190403035741/https://www.skyandtelescope.com/astronomy-resources/how-big-is-a-black-hole/ |url-status=live }}</ref>

[[File:BKL dynamics - video.ogg|thumbtime=0|thumb|alt=A sphere being continuously warped into different ellipsoids, with the direction of the warping constantly changing.|Chaotic oscillations of spacetime experienced by an object approaching a gravitational singularity]]

Observers falling into a Schwarzschild black hole (i.e., non-rotating and not charged) cannot avoid being carried into the singularity once they cross the event horizon.<ref>{{cite journal |last1=Lewis |first1=G. F. |last2=Kwan |first2=J. |title=No Way Back: Maximizing Survival Time Below the Schwarzschild Event Horizon |url=https://www.cambridge.org/core/journals/publications-of-the-astronomical-society-of-australia/article/no-way-back-maximizing-survival-time-below-the-schwarzschild-event-horizon/2A1CCF5CB13E7BEFA6441B3038C635A3 |journal=Publications of the Astronomical Society of Australia |volume=24 |issue=2 |pages=46–52 |date=2007 |doi=10.1071/AS07012 |arxiv=0705.1029 |bibcode=2007PASA...24...46L |s2cid=17261076}}</ref><ref>{{Cite journal |last1=Toporensky |first1=Alexei |last2=Popov |first2=Sergei |title=How to Delay Death and Look Further into the Future If You Fall into a Black Hole |journal=Resonance |date=2023 |url=https://link.springer.com/article/10.1007/s12045-023-1602-8 |volume=28 |issue=5 |pages=737–749 |doi=10.1007/s12045-023-1602-8|url-access=subscription }}</ref> As they fall further into the black hole, they will be torn apart by the growing [[tidal force]]s in a process sometimes referred to as [[spaghettification]] or the ''noodle effect''. Eventually, they will reach the singularity and be crushed into an infinitely small point.<ref name="JCWheeler-2007">{{cite book |last=Wheeler |first=J. Craig | author-link = J. Craig Wheeler |title=Cosmic Catastrophes |edition=2nd |publisher=Cambridge University Press |date=2007 |isbn=978-0-521-85714-7}}</ref>{{rp|p=182}} However, any perturbations, such as those caused by matter or radiation falling in, would cause space to [[BKL singularity|oscillate chaotically]] near the singularity. Any matter falling in would experience intense tidal forces rapidly changing in direction, all while being compressed into an increasingly small volume.<ref>{{Cite book |last1=Belinskii |first1=V.A. |last2=Lifshitz |first2=E.M. |last3=Khalatnikov |first3=I.M. |last4=Agyei |first4=A.K. |title=Perspectives in Theoretical Physics |chapter=The oscillatory mode of approach to a singularity in homogeneous cosmological models with rotating axes |date=1992 |pages=677–689 |doi=10.1016/B978-0-08-036364-6.50048-X |isbn=978-0-08-036364-6 }}</ref><ref name="scienceofinterstellar">{{Cite book |title=The Science of Interstellar |last=Thorne |first=Kip |date=7 November 2014 |publisher=W. W. Norton & Company |isbn=978-0-393-35137-8}}</ref>{{rp|231}}

Alternative forms of general relativity, including addition of some quantum effects, can lead to ''regular'', or ''nonsingular'', black holes without singularities.<ref>{{Cite journal |display-authors=2 |last1=Lan |first1=Chen |last2=Yang |first2=Hao |last3=Guo |first3=Yang |last4=Miao |first4=Yan-Gang |title=Regular Black Holes: A Short Topic Review |journal=International Journal of Theoretical Physics |date=2023 |volume=62 |issue=9 |article-number=202 |doi=10.1007/s10773-023-05454-1 |arxiv=2303.11696 |bibcode=2023IJTP...62..202L }}</ref><ref>{{Cite journal |last1=Olmo |first1=Gonzalo |last2=Rubiera-Garcia |first2=Diego |title=Nonsingular Black Holes in ƒ (R) Theories |journal=Universe |date=2015 |volume=1 |issue=2 |pages=173–185 |doi=10.3390/universe1020173 |arxiv=1509.02430 |bibcode=2015Univ....1..173O |doi-access=free }}</ref> For example, the [[Fuzzball (string theory)|fuzzball]] model, based on [[string theory]], states that black holes are actually made up of [[quantum state|quantum microstates]] and need not have a singularity or an event horizon.<ref>{{cite journal |last=Mathur |first=Samir D. |title=The Fuzzball Proposal for Black Holes: An Elementary Review |journal=Fortschritte der Physik |volume=53 |issue=7–8 |page=793 |date=2005 |doi=10.1002/prop.200410203 |arxiv=hep-th/0502050 |bibcode=2005ForPh..53..793M |s2cid=15083147}}</ref><ref>{{Cite journal |last1=Avery |first1=Steven G. |last2=Chowdhury |first2=Borun D. |last3=Puhm |first3=Andrea |title=Unitarity and Fuzzball Complementarity: "Alice Fuzzes but May Not Even Know It!" |journal=Journal of High Energy Physics |date=2013 |issue=9 |article-number=12 |doi=10.1007/JHEP09(2013)012 |arxiv=1210.6996 |bibcode=2013JHEP...09..012A }}</ref> The theory of [[loop quantum gravity]] proposes that the curvature and density at the center of a black hole is large, but not infinite.<ref>{{Cite journal |last1=Bojowald |first1=Martin |title=Black-Hole Models in Loop Quantum Gravity |journal=Universe |date=2020 |volume=6 |issue=8 |page=125 |doi=10.3390/universe6080125 |arxiv=2009.13565 |bibcode=2020Univ....6..125B |doi-access=free }}</ref>

== Formation ==
Black holes are formed by [[gravitational collapse]] of massive stars, either by direct collapse or during a supernova explosion in a process called ''fallback''.<ref>{{Cite journal |last1=Woosley |first1=S. E. |last2=Heger |first2=A. |last3=Weaver |first3=T. A. |date=7 November 2002 |title=The Evolution and Explosion of Massive Stars |url=https://link.aps.org/doi/10.1103/RevModPhys.74.1015 |journal=Reviews of Modern Physics |language=en |volume=74 |issue=4 |pages=1015–1071 |doi=10.1103/RevModPhys.74.1015 |bibcode=2002RvMP...74.1015W |issn=0034-6861|url-access=subscription }}</ref> Black holes can result from the merger of two [[neutron star]]s or a neutron star and a black hole.<ref>{{Cite journal |display-authors=2 |last1=Zappa |first1=Francesco |last2=Bernuzzi |first2=Sebastiano |last3=Pannarale |first3=Francesco |last4=Mapelli |first4=Michela |last5=Giacobbo |first5=Nicola |date=25 July 2019 |title=Black-Hole Remnants from Black-Hole–Neutron-Star Mergers |url=https://link.aps.org/doi/10.1103/PhysRevLett.123.041102 |journal=Physical Review Letters |language=en |volume=123 |issue=4 |article-number=041102 |doi=10.1103/PhysRevLett.123.041102 |pmid=31491270 |arxiv=1903.11622 |bibcode=2019PhRvL.123d1102Z |issn=0031-9007}}</ref> Other more speculative mechanisms include [[primordial black hole]]s created from density fluctuations in the early universe, the collapse of [[Dark star (Newtonian mechanics)|dark stars]], a hypothetical object powered by annihilation of [[dark matter]], or from hypothetical [[self-interacting dark matter]].<ref>{{Cite journal |last1=Inayoshi |first1=Kohei |last2=Visbal |first2=Eli |last3=Haiman |first3=Zoltán |date=18 August 2020 |title=The Assembly of the First Massive Black Holes |url=https://www.annualreviews.org/content/journals/10.1146/annurev-astro-120419-014455 |journal=Annual Review of Astronomy and Astrophysics |language=en |volume=58 |issue=<!--none--> |pages=27–97 |doi=10.1146/annurev-astro-120419-014455 |arxiv=1911.05791 |bibcode=2020ARA&A..58...27I |issn=0066-4146}}</ref>

=== Supernova ===
Gravitational collapse occurs when an object's internal [[pressure]] is insufficient to resist the object's own gravity. At the end of a star's life, it will run out of [[hydrogen]] to [[nuclear fusion|fuse]], and will start fusing more and more massive elements, until it gets to [[iron]]. Since the fusion of elements heavier than iron would [[endothermic reaction|require more energy than it would release]], nuclear fusion ceases. If the iron core of the star is too massive, the star will no longer be able to support itself and will undergo gravitational collapse.<ref>{{Cite journal |display-authors=2 |last1=Janka |first1=H. |last2=Langanke |first2=K. |last3=Marek |first3=A. |last4=Martinezpinedo |first4=G. |last5=Muller |first5=B. |title=Theory of Core-Collapse Supernovae |journal=Physics Reports |date=2007 |volume=442 |issue=1–6 |pages=38–74 |doi=10.1016/j.physrep.2007.02.002 |arxiv=astro-ph/0612072 |bibcode=2007PhR...442...38J }}</ref><ref>{{Cite journal |last1=Fryer |first1=Chris L. |last2=Holz |first2=Daniel E. |last3=Hughes |first3=Scott A. |title=Gravitational Wave Emission from Core Collapse of Massive Stars |journal=The Astrophysical Journal |date=2002 |volume=565 |issue=1 |pages=430–446 |doi=10.1086/324034 |arxiv=astro-ph/0106113 |bibcode=2002ApJ...565..430F }}</ref>

The mass of a black hole formed via a supernova has a lower bound: if the progenitor star is too small, the collapse may be stopped by the [[Degenerate matter|degeneracy pressure]] of the star's constituents, allowing the condensation of matter into an exotic [[Degenerate matter|denser state]]. Degeneracy pressure occurs from the [[Pauli exclusion principle]]: particles will resist being in the same place as each other. Progenitor stars with masses less than about {{Solar mass|8}} will become [[white dwarf]]s, where the degeneracy pressure of electrons balances gravity. For more massive progenitor stars, the force of gravity overcomes electron degeneracy pressure and the star compresses until [[neutron degeneracy pressure]] resists gravity, forming a [[neutron star]]. If the star is even more massive, neutron degeneracy pressure will not be able to resist the force of gravity and the star will collapse into a black hole.<ref>{{Cite journal |last1=Bennett |first1=Jeffrey |title=Degeneracy Pressure in Stars and Stellar Corpses |journal=The Physics Teacher |date=2025 |volume=63 |issue=3 |pages=212–213 |doi=10.1119/5.0260882 |bibcode=2025PhTea..63c.212B }}</ref><ref name="Carroll-2004">{{cite book |last1=Carroll |first1=Sean M. |author-link=Sean M. Carroll |title=Spacetime and Geometry: An Introduction to General Relativity |title-link=Spacetime and Geometry |date= |publisher=Addison-Wesley |year=2003 |isbn=978-0-8053-8732-2}}, the lecture notes on which the book was based are available for free from Sean Carroll's [https://www.preposterousuniverse.com/spacetimeandgeometry/ website] {{Webarchive|url=https://web.archive.org/web/20170323013522/http://www.preposterousuniverse.com/spacetimeandgeometry/|date=23 March 2017}}</ref>{{rp|loc=5.8}} 

While most of the energy released during gravitational collapse is emitted very quickly, an outside observer does not actually see the end of this process. Even though the collapse takes a finite amount of time from the [[frame of reference|reference frame]] of infalling matter, a distant observer would see the infalling material slow and halt just above the event horizon, due to gravitational time dilation. Light from the collapsing material takes longer and longer to reach the observer, with the delay growing to infinity as the emitting material reaches the event horizon. Thus the external observer never sees the formation of the event horizon; instead, the collapsing material seems to become dimmer and increasingly red-shifted, eventually fading away.<ref>{{cite journal |last1=Penrose |first1=R. |author-link1=Roger Penrose |title=Gravitational Collapse: The Role of General Relativity |journal=General Relativity and Gravitation |volume=34 |issue=7 |page=1141 |date=2002 |doi=10.1023/A:1016578408204 |url=http://www.imamu.edu.sa/Scientific_selections/abstracts/Physics/Gravitational%20Collapse%20The%20Role%20of%20General.pdf |bibcode=2002GReGr..34.1141P |s2cid=117459073|archive-url=https://web.archive.org/web/20130526224126/http://www.imamu.edu.sa/Scientific_selections/abstracts/Physics/Gravitational%20Collapse%20The%20Role%20of%20General.pdf |archive-date=26 May 2013 }}</ref>

=== Other mechanisms ===
Observations of quasars from less than a billion years after the [[Big Bang]]<ref>{{cite journal|display-authors=2|last1=Bañados|first1=Eduardo|last2=Venemans|first2=Bram P.|last3=Mazzucchelli|first3=Chiara|last4=Farina|first4=Emanuele P.|last5=Walter|first5=Fabian |last6=Wang|first6=Feige |last7=Decarli|first7=Roberto |last8=Stern|first8=Daniel |last9=Fan|first9=Xiaohui |last10=Davies|first10=Frederick B. |last11=Hennawi|first11=Joseph F. |date=1 January 2018|title=An 800-Million-Solar-Mass Black Hole in a Significantly Neutral Universe at a Redshift of 7.5|journal=Nature|volume=553|issue=7689|pages=473–476|doi=10.1038/nature25180|pmid=29211709|arxiv=1712.01860|bibcode=2018Natur.553..473B|s2cid=205263326}}</ref><ref>{{Cite journal |last1=Boylan-Kolchin |first1=Michael |last2=Weisz |first2=Daniel R. |title=Uncertain Times: The Redshift–Time Relation from Cosmology and Stars |journal=Monthly Notices of the Royal Astronomical Society |date=2021 |volume=505 |issue=2 |pages=2764–2783 |doi=10.1093/mnras/stab1521 |doi-access=free }}</ref> has led to investigations of other ways to form black holes. The accretion process to build supermassive black holes has a limiting rate of mass accumulation and
a billion years is not enough time to reach quasar status.
One suggestion is [[Direct collapse black hole|direct collapse]] of nearly pure hydrogen gas (low metalicity) clouds characteristic of the young universe, forming a supermassive star which collapses into a black hole.
It has been suggested that seed black holes with typical masses of ~{{Solar mass|{{10^|5}}}} could have formed in this way which then could grow to ~{{Solar mass|{{10^|9}}}}. However, the very large amount of gas required for direct collapse is not typically stable against fragmentation which would form multiple stars. Thus another approach suggests massive star formation followed by collisions that seed massive black holes which ultimately merge to create a quasar.<ref>{{Cite journal |last1=Klessen |first1=Ralf S. |last2=Glover |first2=Simon C. O. |date=August 18, 2023 |title=The First Stars: Formation, Properties, And Impact |url=https://www.annualreviews.org/content/journals/10.1146/annurev-astro-071221-053453 |journal=Annual Review of Astronomy and Astrophysics |language=en |volume=61 |pages=65–130 |doi=10.1146/annurev-astro-071221-053453 |arxiv=2303.12500 |bibcode=2023ARA&A..61...65K |issn=0066-4146}}</ref>{{rp|85}}

A neutron star in a [[common envelope]] with a regular star can accrete sufficient material to collapse to a black hole or two neutron stars can merge. These avenues for the formation of black holes are considered relatively rare.<ref>{{Cite journal |last1=Fryer |first1=Chris L. |last2=Kalogera |first2=Vassiliki |date=June 10, 2001 |title=Theoretical Black Hole Mass Distributions |url=https://iopscience.iop.org/article/10.1086/321359 |journal=The Astrophysical Journal |language=en |volume=554 |issue=1 |pages=548–560 |doi=10.1086/321359 |bibcode=2001ApJ...554..548F |issn=0004-637X}}</ref>

=== Primordial black holes and the Big Bang ===
In the current epoch of the universe, conditions needed to form black holes are rare and are mostly only found in stars. However, in the early universe, conditions may have allowed for black hole formations via other means. Fluctuations of spacetime soon after the Big Bang may have formed areas that were denser than their surroundings. Initially, these regions would not have been compact enough to form a black hole, but eventually, the curvature of spacetime in the regions become large enough to cause them to collapse into a black hole.<ref>{{Cite journal |last1=Yoo |first1=Chul-Moon |title=The Basics of Primordial Black Hole Formation and Abundance Estimation |journal=Galaxies |date=2022 |volume=10 |issue=6 |page=112 |doi=10.3390/galaxies10060112 |arxiv=2211.13512 |bibcode=2022Galax..10..112Y |doi-access=free }}</ref><ref>{{Cite web |title=Primordial Black Holes |url=https://svs.gsfc.nasa.gov/14524/ |last=Balzer |first=Ashley |date=2024-05-07 |url-status=live |archive-url=https://web.archive.org/web/20250827012141/https://svs.gsfc.nasa.gov/14524/ |archive-date=2025-08-27 |access-date=2025-11-23 |website=NASA SVS}}</ref> Different models for the early universe vary widely in their predictions of the scale of these fluctuations. Various models predict the creation of primordial black holes ranging from a [[Planck mass]] (~{{val|2.2|e=-8|u=kg}}) to hundreds of thousands of solar masses.<ref name="carr primordial">{{Cite conference |title=Primordial Black Holes: Do They Exist and Are They Useful? |conference=59th Yamada Conference on Inflating Horizon of Particle Astrophysics and Cosmology |last=Carr |first=Bernard |date=2025-11-26 |arxiv=astro-ph/0511743 }}</ref><ref>{{Cite journal|display-authors=2|last1=Pacucci |first1=Fabio |last2=Ferrara |first2=Andrea |last3=Grazian |first3=Andrea |last4=Fiore |first4=Fabrizio |last5=Giallongo |first5=Emanuele |last6=Puccetti |first6=Simonetta |title=First Identification of Direct Collapse Black Hole Candidates in the Early Universe in CANDELS/GOODS-S |journal=Monthly Notices of the Royal Astronomical Society |pages=astro–ph/0511743 |publisher=Universal Academy Press |date=2005 |volume=459 |issue=2 |doi=10.1093/mnras/stw725 |doi-access=free |isbn=978-4-946443-94-7 |arxiv=astro-ph/0511743 |bibcode=2005astro.ph.11743C}}</ref> Primordial black holes with masses less than {{val|e=12|u=kg}} would have evaporated by now due to Hawking radiation.<ref name="Carr" />

Despite the early universe being extremely [[density|dense]], it did not re-collapse into a black hole during the Big Bang, since the universe was expanding rapidly and did not have the gravitational differential necessary for black hole formation. Models for the gravitational collapse of objects of relatively constant size, such as [[star]]s, do not necessarily apply in the same way to rapidly expanding space such as the Big Bang.<ref>{{multiref2|{{cite web |author1=Philip Gibbs |title=Is the Big Bang a Black Hole? |url=http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/universe.html |publisher=[[John Baez]] | access-date=16 March 2018 |archive-date=31 December 2018 |archive-url=https://web.archive.org/web/20181231021714/http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/universe.html |url-status=live }}|{{Cite web |title=Why Didn't the Infant Universe Collapse into a Black Hole? |url=https://www.space.com/why-infant-universe-not-collapse-black-hole |last=Sutter |first=Paul |date=2023-06-21 |url-status=live |archive-url=https://web.archive.org/web/20250325152015/https://www.space.com/why-infant-universe-not-collapse-black-hole |archive-date=2025-03-25 |access-date=2025-11-24 |website=Space.com}}|{{Cite web |title=According to the Big Bang Theory, All the Matter in the Universe Erupted from a Singularity. Why Didn't All This Matter—Cheek by Jowl as It Was—Immediately Collapse into a Black Hole? |url=https://www.scientificamerican.com/article/according-to-the-big-bang/ |last=Musser |first=George |date=2003-09-22 |url-status=live |archive-url=https://web.archive.org/web/20250426033551/https://www.scientificamerican.com/article/according-to-the-big-bang/ |archive-date=2025-04-26 |access-date=2025-11-24 |website=Scientific American}}}}</ref>

=== High-energy collisions ===
In principle, black holes could be formed in [[high-energy physics|high-energy]] particle collisions that achieve sufficient density, although no such events have been detected.<ref>{{Cite journal |last1=Kaloper |first1=Nemanja |last2=Terning |first2=John |title=How Black Holes Form in High Energy Collisions |journal=General Relativity and Gravitation |date=2007 |volume=39 |issue=10 |pages=1525–1532 |doi=10.1007/s10714-007-0468-5 |arxiv=0705.0408 |bibcode=2007GReGr..39.1525K }}</ref><ref>{{Cite journal |last1=Giddings |first1=S. B. |last2=Thomas |first2=S. |title=High Energy Colliders as Black Hole Factories: The End of Short Distance Physics |date=2002 |journal=Physical Review D |volume=65 |issue=5 |article-number=056010 |doi=10.1103/PhysRevD.65.056010 |arxiv=hep-ph/0106219|bibcode=2002PhRvD..65e6010G|s2cid=1203487 }}</ref>
These hypothetical [[micro black hole]]s, which could form from the collision of [[cosmic ray]]s and Earth's atmosphere or in [[particle accelerator]]s like the [[Large Hadron Collider]], would not be able to aggregate additional mass.<ref name="LHCsafety">{{cite journal |url=http://lsag.web.cern.ch/lsag/LSAG-Report.pdf |title=Review of the Safety of LHC Collisions |journal=Journal of Physics G: Nuclear Physics |volume=35 |issue=11 |article-number=115004 |author=LHC Safety Assessment Group |url-status=live |archive-url=https://web.archive.org/web/20100414160742/http://lsag.web.cern.ch/lsag/LSAG-Report.pdf |archive-date=14 April 2010 |bibcode=2008JPhG...35k5004E |year=2008 |arxiv=0806.3414 |doi=10.1088/0954-3899/35/11/115004|s2cid=53370175 }}</ref> Instead, they would [[black hole evaporation|evaporate]] in about 10{{sup|−25}} seconds, posing no threat to the Earth.<ref>{{cite journal |last1=Peskin |first1=M. E. |title=The End of the World at the Large Hadron Collider? |journal=Physics |volume=1 |article-number=14 |date=2008 |doi=10.1103/Physics.1.14 |bibcode=2008PhyOJ...1...14P|doi-access=free}}</ref>

== Evolution ==
After a black hole forms, it may change through phenomena such as [[black hole merger|mergers]], [[accretion (astrophysics)|accretion of matter]], and evaporation via [[Hawking radiation]].

=== Merger ===
[[File:BBH gravitational lensing of gw150914.webm|alt=A simulation of two black holes colliding to form a super massive black hole|thumb|Simulation of two black holes colliding]]

Black holes can merge with other objects such as stars or [[binary black hole|other black holes]]. This is thought to have been important, especially in the early growth of supermassive black holes, which could have formed from the aggregation of many smaller objects.<ref name="ReesVolonteri">{{cite conference |first1=M. J. |series=Proceedings of the International Astronomical Union |last1=Rees |first2=M. |last2=Volonteri |author2-link=Marta Volonteri|title=Massive Black Holes: Formation and Evolution |editor1-first=V. |editor1-last=Karas |editor2-first=G. |editor2-last=Matt |book-title=Black Holes from Stars to Galaxies—Across the Range of Masses |pages=51–58 |date=2007 |isbn=978-0-521-86347-6 |arxiv=astro-ph/0701512 |bibcode=2007IAUS..238...51R |doi=10.1017/S1743921307004681 |doi-access=free |s2cid=14844338 }}</ref> The process has also been proposed as the origin of some intermediate-mass black holes.<ref>{{cite journal |last1=Zwart |first1=S. F. P. |last2=Baumgardt |first2=H. |last3=Hut |first3=P. |last4=Makino |first4=J. |last5=McMillan |first5=S. L. W. |display-authors=2 |title=Formation of Massive Black Holes Through Runaway Collisions in Dense Young Star Clusters |journal=Nature |volume=428 |issue=6984 |date=2004 |doi=10.1038/nature02448 |pmid=15085124 |arxiv=astro-ph/0402622 |bibcode=2004Natur.428..724P |pages=724–726 |s2cid=4408378}}</ref><ref>{{cite journal |display-authors=2 |last1=O'Leary |first1=R. M. |last2=Rasio |first2=F. A. |last3=Fregeau |first3=J. M. |last4=Ivanova |first4=N. |last5=o'Shaughnessy |first5=R. |title=Binary Mergers and Growth of Black Holes in Dense Star Clusters |journal=The Astrophysical Journal |volume=637 |issue=2 |pages=937–951 |date=2006 |doi=10.1086/498446 |arxiv=astro-ph/0508224 |bibcode=2006ApJ...637..937O |s2cid=1509957}}</ref> Mergers of supermassive black holes may take a long time: As a binary of supermassive black holes approach each other, most nearby stars are [[gravitational slingshot|slingshotted]] away, leaving little for the black holes to gravitationally interact with that would allow them to get closer to each other. This phenomenon has been called the [[final parsec problem]], as the distance at which this happens is usually around one [[parsec]].<ref>{{Cite journal |display-authors=2 |last1=Ryu |first1=Taeho |last2=Perna |first2=Rosalba |last3=Haiman |first3=Zoltán |last4=Ostriker |first4=Jeremiah P. |last5=Stone |first5=Nicholas C. |title=Interactions Between Multiple Supermassive Black Holes in Galactic Nuclei: A Solution to the Final Parsec Problem |journal=Monthly Notices of the Royal Astronomical Society |date=2018 |volume=473 |issue=3 |pages=3410–3433 |doi=10.1093/mnras/stx2524 |doi-access=free }}</ref><ref>{{Cite journal |last1=Vasiliev |first1=Eugene |last2=Antonini |first2=Fabio |last3=Merritt |first3=David |title=The Final-Parsec Problem in Nonspherical Galaxies Revisited |journal=The Astrophysical Journal |date=2014 |volume=785 |issue=2 |page=163 |doi=10.1088/0004-637X/785/2/163 |arxiv=1311.1167 |bibcode=2014ApJ...785..163V }}</ref>

=== Accretion of matter ===
{{See also|Accretion disk}}
[[File:Centaurus A- A Nearby Elliptical Galaxy With An Active Galactic Nucleus (2001-0157blue - 0157blue xray).tiff|thumb|alt=An image, all blue, of Centaurus A's active galactic nucleus as a bright spot in the center with a bright relativistic jet going away from it.|The active galactic nucleus of galaxy [[Centaurus A]] in X-ray light, believed to be powered by a supermassive black hole (centre) and surrounded by x-ray binaries (blue dots)]]

When a black hole [[accretion (astrophysics)|accretes]] matter, the gas in the inner accretion disk orbits at very high speeds because of its proximity to the black hole. The resulting [[friction]] heats the inner disk to temperatures at which it emits vast amounts of electromagnetic radiation (mainly [[X-ray]]s) detectable by telescopes. By the time the matter of the disk reaches the [[Innermost stable circular orbit|ISCO]], between 5.7% and 42% of its [[mass-energy equivalence|mass will have been converted to energy]], depending on the black hole's spin. About 90% of this energy is released within 20 black hole radii.<ref name="McClintockRemillard2006">{{cite book |last1=McClintock |first1=J. E. |last2=Remillard |first2=R. A. |chapter=Black Hole Binaries |editor1-first=W. |editor1-last=Lewin|editor2-first=M. |editor2-last=van der Klis |title=Compact Stellar X-Ray Sources |page=157 |date=2006 |isbn=978-0-521-82659-4 |arxiv=astro-ph/0306213 |bibcode=2006csxs.book..157M}} section 4.1.5.</ref> In many cases, accretion disks are accompanied by [[relativistic jets]] that are emitted along the black hole's poles, which carry away much of the energy.<ref>{{Cite journal |last1=Kuroda |first1=Takami |last2=Shibata |first2=Masaru |title=Numerical Relativity Simulations of Black Hole and Relativistic Jet Formation |journal=Monthly Notices of the Royal Astronomical Society: Letters |date=2024 |volume=533 |pages=L107–L112 |doi=10.1093/mnrasl/slae069 |doi-access=free }}</ref>

Many of the universe's most energetic phenomena have been attributed to the accretion of matter on black holes. [[Active galactic nuclei]] and [[quasar]]s are powered by accretion onto supermassive black holes.<ref>{{Cite journal |last1=Saikia |first1=D. J. |title=Jets in Radio Galaxies and Quasars: An Observational Perspective |journal=Journal of Astrophysics and Astronomy |date=2022 |volume=43 |issue=2 |article-number=97 |doi=10.1007/s12036-022-09863-2 |arxiv=2206.05803 }}</ref><ref>{{Cite journal |display-authors=2 |last1=Czerny |first1=Bożena |last2=Cao |first2=Shulei |last3=Jaiswal |first3=Vikram Kumar |last4=Karas |first4=Vladimír |last5=Khadka |first5=Narayan |last6=Martínez-Aldama |first6=Mary Loli |last7=Naddaf |first7=Mohammad Hassan |last8=Panda |first8=Swayamtrupta |last9=Pozo Nuñez |first9=Francisco |last10=Prince |first10=Raj |last11=Ratra |first11=Bharat |last12=Sniegowska |first12=Marzena |last13=Yu |first13=Zhefu |last14=Zajaček |first14=Michal |title=Accretion Disks, Quasars and Cosmology: Meandering Towards Understanding |journal=Astrophysics and Space Science |date=2023 |volume=368 |issue=2 |article-number=8 |doi=10.1007/s10509-023-04165-7}}</ref> [[X-ray binaries]] are generally accepted to be [[binary star|binary]] systems in which one of the two objects is a [[compact object]] accreting matter from its companion.<ref name="CMS1999" /> [[Ultraluminous X-ray source]]s may be the accretion disks of intermediate-mass black holes.<ref>{{cite journal |display-authors=2 |last1=Winter |first1=L. M. |last2=Mushotzky |first2=R. F. |last3=Reynolds |first3=C. S. |title=XMM-Newton Archival Study of the Ultraluminous X-Ray Population in Nearby Galaxies |date=2006 |journal=The Astrophysical Journal |volume=649 |issue=2 |pages=730–752 |arxiv=astro-ph/0512480 |doi=10.1086/506579|bibcode=2006ApJ...649..730W|s2cid=118445260 }}</ref>

At a certain rate of accretion, the outward radiation pressure will become as strong as the inward gravitational force, and the black hole should, in theory, be unable to accrete any faster. This limit is called the [[Eddington limit]]. Realistically, many black holes accrete beyond this rate due to their non-spherical geometry or instabilities in the accretion disk. Accretion beyond the limit is called [[super-Eddington accretion]] and may have been commonplace in the early universe.<ref>{{Cite journal |display-authors=2 |last1=Brightman |first1=M. |last2=Bachetti |first2=M. |last3=Earnshaw |first3=H. P. |last4=Fürst |first4=F. |last5=García |first5=J. |last6=Grefenstette |first6=B. |last7=Heida |first7=M. |last8=Kara |first8=E. |last9=Madsen |first9=K. K. |last10=Middleton |first10=M. J. |last11=Stern |first11=D. |last12=Tombesi |first12=F. |last13=Walton |first13=D. J. |title=Breaking the Limit: Super-Eddington Accretion Onto Black Holes and Neutron Stars |journal=Bulletin of the American Astronomical Society |date=2019 |volume=51 |issue=3 |page=352 |arxiv=1903.06844 |bibcode=2019BAAS...51c.352B }}</ref><ref name="Regan">{{Cite journal |display-authors=2 |last1=Regan |first1=John A. |last2=Downes |first2=Turlough P. |last3=Volonteri |first3=Marta |last4=Beckmann |first4=Ricarda |last5=Lupi |first5=Alessandro |last6=Trebitsch |first6=Maxime |last7=Dubois |first7=Yohan |title=Super-Eddington Accretion and Feedback from the First Massive Seed Black Holes |journal=Monthly Notices of the Royal Astronomical Society |date=2019 |volume=486 |issue=3 |pages=3892–3906 |doi=10.1093/mnras/stz1045 |doi-access=free }}</ref>

Stars have been observed to get torn apart by tidal forces in the immediate vicinity of supermassive black holes in galaxy nuclei, in what is known as a [[tidal disruption event]] (TDE). Some of the material from the disrupted star forms an accretion disk around the black hole, which emits observable electromagnetic radiation.<ref>{{Cite journal |last1=Evans |first1=Charles R. |last2=Kochanek |first2=Christopher S. |title=The Tidal Disruption of a Star by a Massive Black Hole |journal=The Astrophysical Journal |date=1989 |volume=346 |pages=L13 |doi=10.1086/185567 |bibcode=1989ApJ...346L..13E }}</ref><ref>{{Cite journal |last1=Komossa |first1=S. |title=Tidal Disruption of Stars by Supermassive Black Holes: Status of Observations |journal=Journal of High Energy Astrophysics |date=2015 |volume=7 |pages=148–157 |doi=10.1016/j.jheap.2015.04.006 |arxiv=1505.01093 |bibcode=2015JHEAp...7..148K }}</ref>

=== Interaction with galaxies ===
The correlation between the masses of supermassive black holes in the centres of galaxies with the [[M-sigma relation|velocity dispersion]] and mass of stars in their [[galactic bulge|host bulges]] suggests that the formation of galaxies and the formation of their central black holes are related. Black hole [[cosmic wind|winds]] from rapid accretion, particularly when the galaxy itself is still accreting matter, can compress gas nearby, accelerating star formation. However, if the winds become too strong, the black hole may blow nearly all of the gas out of the galaxy, quenching star formation. Black hole jets may also energise nearby [[stellar-wind bubble|cavities]] of plasma and eject low-[[entropy]] gas from out of the galactic core, causing gas in galactic centers to be [[Cooling flow#Cooling flow problem|hotter than expected]].<ref>{{Cite journal |display-authors=2 |last1=Cattaneo |first1=A. |last2=Faber |first2=S. M. |last3=Binney |first3=J. |last4=Dekel |first4=A. |last5=Kormendy |first5=J. |last6=Mushotzky |first6=R. |last7=Babul |first7=A. |last8=Best |first8=P. N. |last9=Brüggen |first9=M. |last10=Fabian |first10=A. C. |last11=Frenk |first11=C. S. |last12=Khalatyan |first12=A. |last13=Netzer |first13=H. |last14=Mahdavi |first14=A. |last15=Silk |first15=J. |last16=Steinmetz |first16=M. |last17=Wisotzki |first17=L. |title=The Role of Black Holes in Galaxy Formation and Evolution |journal=Nature |date=2009 |volume=460 |issue=7252 |pages=213–219 |doi=10.1038/nature08135 |pmid=19587763 |arxiv=0907.1608 }}</ref>

=== Evaporation ===
{{Main|Hawking radiation}}

If Hawking's theory of black hole radiation is correct, then black holes are expected to shrink and evaporate over time as they lose mass by the emission of photons and other particles.<ref name="Hawking1974" /> The temperature of this thermal spectrum ([[Hawking temperature]]) is proportional to the surface gravity of the black hole, which is inversely proportional to the mass. Hence, large black holes emit less radiation than small black holes.<ref name="Carroll-2004" />{{rp|loc=Ch. 9.6}}<ref>{{Cite journal |last1=Ruiz |first1=O. |last2=Molina |first2=U. |last3=Viloria |first3=P. |title=Thermodynamic Analysis of Kerr-Newman Black Holes |journal=Journal of Physics: Conference Series |date=2019 |volume=1219 |issue=1 |article-number=012016 |doi=10.1088/1742-6596/1219/1/012016 |bibcode=2019JPhCS1219a2016R |quote=From this, an expression is established for the Hawking temperature of a Kerr-Newman black hole as a function of its mass 𝑀, angular moment 𝐽 and load 𝑄. As the black hole loses mass, its temperature increases inversely proportional.}}</ref> A stellar black hole of {{Solar mass|1}} has a Hawking temperature of 62&nbsp;[[nanokelvin]]s.<ref>{{cite news |last1=Siegel |first1=Ethan |author-link1=Ethan Siegel |title=Ask Ethan: Do Black Holes Grow Faster Than They Evaporate? |url=https://www.forbes.com/sites/startswithabang/2017/08/19/ask-ethan-do-black-holes-grow-faster-than-they-evaporate/ |access-date=17 March 2018 |work=Forbes ("Starts With A Bang" blog) |date=2017 |archive-date=22 November 2018 |archive-url=https://web.archive.org/web/20181122031830/https://www.forbes.com/sites/startswithabang/2017/08/19/ask-ethan-do-black-holes-grow-faster-than-they-evaporate/ |url-status=live }}</ref> This is far less than the 2.7&nbsp;K temperature of the [[cosmic microwave background]] radiation. Stellar-mass or larger black holes receive more mass from the cosmic microwave background than they emit through Hawking radiation and thus will grow instead of shrinking.<ref>{{cite journal |last1=Sivaram |first1=C. |title=Black Hole Hawking Radiation May Never Be Observed! |journal=General Relativity and Gravitation |date=2001 |volume=33 |issue=2 |pages=175–181 |bibcode=2001GReGr..33..175S |doi=10.1023/A:1002753400430|s2cid=118913634 }}</ref> To have a Hawking temperature larger than 2.7&nbsp;K (and be able to evaporate), a black hole would need a mass less than the [[Moon]]. Such a black hole would have a diameter of less than a tenth of a millimetre.<ref>{{cite web |url=http://www.einstein-online.info/elementary/quantum/evaporating_bh/?set_language=en |title=Evaporating Black Holes? |website=Einstein online |publisher=Max Planck Institute for Gravitational Physics |date=2010 |access-date=12 December 2010 |archive-url=https://web.archive.org/web/20110722055345/http://www.einstein-online.info/elementary/quantum/evaporating_bh/?set_language=en |archive-date=22 July 2011}}</ref>

The Hawking radiation for an astrophysical black hole is predicted to be very weak and would thus be exceedingly difficult to detect from Earth. A possible exception is the [[microsecond]]-long burst of [[gamma ray]]s emitted in the last stage of the evaporation of primordial black holes. Searches for such flashes have proven unsuccessful and provide stringent limits on the possibility of existence of low mass primordial black holes, with modern research predicting that primordial black holes must make up less than a fraction of {{val|e=-7}} of the universe's total mass.<ref>{{cite journal |display-authors=2 |last1=Fichtel |first1=C. E. |last2=Bertsch |first2=D. L. |last3=Dingus |first3=B. L.|author3-link= Brenda Dingus |last4=Esposito |first4=J. A. |last5=Hartman |first5=R. C. |last6=Hunter |first6=S. D. |last7=Kanbach |first7=G. |last8=Kniffen |first8=D. A. |last9=Lin |first9=Y. C. |title=Search of the Energetic Gamma-Ray Experiment Telescope (EGRET) Data for High-Energy Gamma-Ray Microsecond Bursts |journal=Astrophysical Journal |volume=434 |issue=2 |pages=557–559 |date=1994 |doi=10.1086/174758|bibcode=1994ApJ...434..557F |last10=Mattox |first10=J. R. |last11=Mayer-Hasselwander |first11=H. A. |last12=McDonald |first12=L. |last13=Michelson |first13=P. F. |last14=Von Montigny |first14=C. |last15=Nolan |first15=P. L. |last16=Schneid |first16=E. J. |last17=Sreekumar |first17=P. |last18=Thompson |first18=D. J.}}</ref><ref name="Carr" /> NASA's [[Fermi Gamma-ray Space Telescope]], launched in 2008, has searched for these flashes, but has not yet found any.<ref>{{cite web |first=R. |last=Naeye |title=Testing Fundamental Physics |url=http://www.nasa.gov/mission_pages/GLAST/science/testing_fundamental_physics.html |publisher=NASA |access-date=16 September 2008 |url-status=live |archive-url=https://web.archive.org/web/20080831045232/http://www.nasa.gov/mission_pages/GLAST/science/testing_fundamental_physics.html |archive-date=31 August 2008}}</ref><ref>{{Cite journal |last1=Federico |first1=Kevin |last2=Profumo |first2=Stefano |title=Black Hole Explosions as Probes of New Physics |journal=Physical Review D |date=2025 |volume=111 |issue=6 |article-number=063006 |doi=10.1103/PhysRevD.111.063006}}</ref>

=== Laws of mechanics and thermodynamics ===
{{Main|Black hole thermodynamics}}

[[File:Bekenstein-Hawking entropy of a black hole.svg|thumb|alt=A geodesic sphere made up of triangles labelled as the black hole event horizon. Each triangle is labelled as "one Planck area" and "one unit of entropy".|A black hole's entropy [[Direct proportionality|scales]] with the surface area of its event horizon.]]
When based in general relativity, the constraints on a black hole's properties are called the [[laws of black hole mechanics]]. For a black hole that is not still forming or accreting matter, the zeroth law of black hole mechanics states the black hole's [[surface gravity]] is constant across the event horizon. The first law relates changes in the black hole's surface area, angular momentum, and charge to changes in its energy. The second law says the surface area of a black hole never decreases on its own. Finally, the third law says that the surface gravity of a black hole is never zero. These laws are mathematical analogues of the [[laws of thermodynamics]]. They are not equivalent, however, because, according to general relativity without quantum mechanics, a black hole can never emit radiation, and thus its temperature must always be zero.<ref name="WaldLiving">{{cite journal |last=Wald |first=Robert M. |date=2001 |title=The Thermodynamics of Black Holes |journal=Living Reviews in Relativity |volume=4 |issue=1 |article-number=6 |doi=10.12942/lrr-2001-6 |doi-access=free |issn=1433-8351 |pmc=5253844 |pmid=28163633 |arxiv=gr-qc/9912119 |bibcode=2001LRR.....4....6W }}</ref>{{rp|11}}<ref name="carlip14">{{Cite journal |last1=Carlip |first1=S. |title=Black Hole Thermodynamics |journal=International Journal of Modern Physics D |date=2014 |volume=23 |issue=11 |doi=10.1142/S0218271814300237 |arxiv=1410.1486 }}</ref>

Quantum mechanics predicts that a black hole will continuously emit thermal Hawking radiation, and therefore must always have a nonzero temperature. It also predicts that all black holes have [[entropy]] which scales with their surface area. When quantum mechanics is accounted for, the laws of black hole mechanics become equivalent to the classical laws of thermodynamics.<ref name="WaldLiving" /><ref>{{Cite journal |last1=Witten |first1=Edward |title=Introduction to Black Hole Thermodynamics |journal=The European Physical Journal Plus |date=2025 |volume=140 |issue=5 |article-number=430 |doi=10.1140/epjp/s13360-025-06288-y}}</ref> However, these conclusions are derived without a complete theory of quantum gravity, although many potential theories do predict black holes having entropy and temperature. Thus, the true quantum nature of black hole thermodynamics continues to be debated.<ref name="WaldLiving" />{{rp|29}}<ref name="carlip14" />

== Observational evidence ==
Millions of black holes derived from stellar collapse are expected to exist in the Milky Way. Even a [[dwarf galaxy]] like [[Draco (dwarf galaxy)|Draco]] should have hundreds.<ref>{{Cite journal |last1=Elbert |first1=Oliver D. |last2=Bullock |first2=James S. |last3=Kaplinghat |first3=Manoj |date=1 January 2018 |title=Counting Black Holes: The Cosmic Stellar Remnant Population and Implications for LIGO |url=https://academic.oup.com/mnras/article/473/1/1186/4060726 |journal=Monthly Notices of the Royal Astronomical Society |language=en |volume=473 |issue=1 |pages=1186–1194 |doi=10.1093/mnras/stx1959 |doi-access=free |issn=0035-8711|arxiv=1703.02551 }}</ref> Only a few of these have been detected.
By nature, black holes do not themselves emit any electromagnetic radiation other than the hypothetical, typically extremely weak Hawking radiation, so astrophysicists searching for black holes must rely on indirect observations. The defining characteristic of a black hole is its event horizon. The horizon itself cannot be imaged,<ref>{{Cite journal |last1=Abramowicz |first1=M. A. |last2=Kluźniak |first2=W. |last3=Lasota |first3=J.-P. |date=December 2002 |title=No Observational Proof of the Black-Hole Event-Horizon |url=http://www.aanda.org/10.1051/0004-6361:20021645 |journal=Astronomy & Astrophysics |volume=396 |issue=3 |pages=L31–L34 |doi=10.1051/0004-6361:20021645 |arxiv=astro-ph/0207270 |bibcode=2002A&A...396L..31A |issn=0004-6361}}</ref> so all other possible explanations for these indirect observations must be considered and eliminated before concluding that a black hole has been observed.<ref>{{Cite journal |display-authors=1 |last1=Event Horizon Telescope Collaboration |last2=Akiyama |first2=Kazunori |last3=Alberdi |first3=Antxon |last4=Alef |first4=Walter |last5=Algaba |first5=Juan Carlos |last6=Anantua |first6=Richard |last7=Asada |first7=Keiichi |last8=Azulay |first8=Rebecca |last9=Bach |first9=Uwe |last10=Baczko |first10=Anne-Kathrin |last11=Ball |first11=David |last12=Baloković |first12=Mislav |last13=Barrett |first13=John |last14=Bauböck |first14=Michi |last15=Benson |first15=Bradford A. |date=May 2022 |title=First Sagittarius A* Event Horizon Telescope Results. VI. Testing the Black Hole Metric |journal=The Astrophysical Journal Letters |volume=930 |issue=2 |pages=L17 |doi=10.3847/2041-8213/ac6756 |doi-access=free |bibcode=2022ApJ...930L..17E |issn=2041-8205}}</ref>{{rp|11}}

=== Direct interferometry ===
{{Multiple image
| image1            = A view of the M87 supermassive black hole in polarised light.tif
| width1            = 120
| alt1              = An orange donut of gases surrounding a black hole, with lines superimposed over the gases
| caption1          = An [[M87*]] image with superimposed lines representing the magnitude and direction of polarisation
| image2            = A view of the jet and shadow of M87’s black hole (eso2305a).jpg
| width2            = 120
| alt2              = M87* with a long relativistic jet extending from it. The Event Horizon Telescope image of the black hole is inset.
| caption2          = The M87* relativistic jet; inset is the black hole shadow
}}

The [[Event Horizon Telescope]] (EHT) is a global system of radio telescopes capable of directly observing a black hole shadow.<ref name="APJL-20190410" /> The [[angular resolution]] of a telescope is based on its [[aperture]] and the wavelengths it is observing. Because the [[angular diameter]]s of Sagittarius A* and Messier 87* in the sky are very small, a single telescope would need to be about the size of the Earth to clearly distinguish their horizons using radio wavelengths. By combining data from several different radio telescopes around the world, the Event Horizon Telescope creates an effective aperture the diameter size of the Earth. The EHT team used [[CLEAN (algorithm)|imaging algorithms]] to compute the most probable image from the data in its [[History of black hole physics#EHT|observations of Sagittarius A* and M87*]].<ref>{{Cite journal |last1=Akiyama |first1=Kazunori |last2=Alberdi |first2=Antxon |last3=Alef |first3=Walter |last4=Asada |first4=Keiichi |last5=Azulay |first5=Rebecca |last6=Baczko |first6=Anne-Kathrin |last7=Ball |first7=David |last8=Baloković |first8=Mislav |last9=Barrett |first9=John |last10=Bintley |first10=Dan |last11=Blackburn |first11=Lindy |last12=Boland |first12=Wilfred |last13=Bouman |first13=Katherine L. |last14=Bower |first14=Geoffrey C. |last15=Bremer |first15=Michael |last16=Brinkerink |first16=Christiaan D. |last17=Brissenden |first17=Roger |last18=Britzen |first18=Silke |last19=Broderick |first19=Avery E. |last20=Broguiere |first20=Dominique |last21=Bronzwaer |first21=Thomas |last22=Byun |first22=Do-Young |last23=Carlstrom |first23=John E. |last24=Chael |first24=Andrew |last25=Chan |first25=Chi-Kwan |last26=Chatterjee |first26=Shami |last27=Chatterjee |first27=Koushik |last28=Chen |first28=Ming-Tang |last29=Chen 陈 |first29=Yongjun 永军 |last30=Cho |first30=Ilje |display-authors=2 |title=First M87 Event Horizon Telescope Results. II. Array and Instrumentation |journal=The Astrophysical Journal Letters |date=2019 |volume=875 |pages=L2 |doi=10.3847/2041-8213/ab0c96 |doi-access=free }}</ref><ref name="eht19" />

=== Gravitational waves ===
[[Gravitational-wave interferometry]] can be used to detect merging black holes and other compact objects. In this method, a laser beam is split, sent down two long arms of a tunnel, then reflected at the far end of the tunnels to reconverge at the intersection of the arms, precisely [[destructive interference|cancelling each other]]. However, when a gravitational wave passes, it warps spacetime, changing the relative lengths of the arms themselves. Since each laser beam is now travelling a slightly different distance, they do not cancel out and produce a recognisable signal. Analysis of the signal can give scientists information about what caused the gravitational waves. Since gravitational waves are very weak, gravitational-wave observatories such as [[LIGO]] must have arms several kilometres long and carefully control for [[seismic noise|noise]] from Earth to be able to detect these gravitational waves.<ref>{{Cite web |title=FAQ |url=https://www.ligo.caltech.edu/page/faq |url-status=live |archive-url=https://web.archive.org/web/20260113010624/https://www.ligo.caltech.edu/page/faq |archive-date=2026-01-13 |access-date=2026-02-05 |website=LIGO Lab}}</ref> Since [[History of black hole physics#LIGO|the first measurements in 2016]], multiple gravitational waves from black holes have been detected and analysed.<ref name="reynolds21" />

=== Stars orbiting Sagittarius A* ===
{{Main|Sagittarius A* cluster}}

[[File:SgrA2021 video.ogg|thumb|alt=Several stars, represented by white dots, moving around a central object (Sagittarius A*). The background switches between images taken of the area over various years.|Stars moving around Sagittarius A*, as seen in 2021]]

The [[proper motion]]s of stars near the centre of the Milky Way provide strong observational evidence that these stars are orbiting a supermassive black hole.<ref name="Gillessen">{{cite journal |last1=Gillessen |first1=S. |last2=Eisenhauer |first2=F. |last3=Trippe |first3=S. |last4=Alexander |first4=T. |last5=Genzel |first5=R. |last6=Martins |first6=F. |last7=Ott |first7=T. |display-authors=2 |title=Monitoring Stellar Orbits Around the Massive Black Hole in the Galactic Center |journal=The Astrophysical Journal |volume=692 |issue=2 |pages=1075–1109 |date=2009 |doi=10.1088/0004-637X/692/2/1075 |arxiv=0810.4674 |bibcode=2009ApJ...692.1075G |s2cid=1431308}}</ref> Astronomers have tracked the motions of 90 stars orbiting an invisible object coincident with the radio source Sagittarius A*. One of the stars—called [[S2 (star)|S2]]—completed a full orbit.  By fitting the motions of stars to [[Keplerian orbit]]s, the astronomers were able to infer that the invisible object assumed to be Sagittarius A* must have a mass of {{Solar mass|{{val|4.3e6}}}}, with a radius of less than 0.002 light-years.<ref name="Gillessen" /> This upper limit radius is larger than the Schwarzschild radius for the estimated mass, so the combination does not prove Sagittarius A* is a black hole. Nevertheless, these observations strongly suggest that the central object is a supermassive black hole as there are no other plausible scenarios for confining so much invisible mass into such a small volume.<ref name="Ghez1998">{{cite journal |last1=Ghez |first1=A. M. |last2=Klein |first2=B. L. |last3=Morris |first3=M. |last4=Becklin |first4=E. E. |display-authors=2 |title=High Proper-Motion Stars in the Vicinity of Sagittarius A*: Evidence for a Supermassive Black Hole at the Center of Our Galaxy |journal=The Astrophysical Journal |volume=509 |issue=2 |pages=678–686 |date=1998 |doi=10.1086/306528 |arxiv=astro-ph/9807210 |bibcode=1998ApJ...509..678G |s2cid=18243528}}</ref> Additionally, luminosity data from this object implies it must possess an event horizon, a defining feature of black holes.<ref>{{Cite journal |title=The Event Horizon of Sagittarius A* |last1=Broderick |first1=Avery |date=August 2009 |journal=The Astrophysical Journal |doi=10.1088/0004-637X/701/2/1357 |last2=Loeb |first2=Abraham |last3=Narayan |first3=Ramesh |volume=701 |issue=2 |pages=1357–1366 |arxiv=0903.1105 |bibcode=2009ApJ...701.1357B|s2cid=12991878 }}</ref> The Event Horizon Telescope image of Sagittarius A*, released in 2022, provided further confirmation that it is indeed a black hole.<ref name="eht-press-release">{{Cite web |title=Astronomers Reveal First Image of the Black Hole at the Heart of Our Galaxy |url=https://eventhorizontelescope.org/blog/astronomers-reveal-first-image-black-hole-heart-our-galaxy |date=2022-05-12 |url-status=live |archive-url=https://web.archive.org/web/20250926081853/https://eventhorizontelescope.org/blog/astronomers-reveal-first-image-black-hole-heart-our-galaxy |archive-date=2025-09-26 |access-date=2025-12-02 |website=[[Event Horizon Telescope]]}}</ref>

=== Binaries ===
{{See also|X-ray binary}}
[[File:Chandra image of Cygnus X-1.jpg|thumb|alt=Black hole Cygnus X-1 as seen by the Chandra X-Ray Observatory, a bright spot over a black background.|A [[Chandra X-Ray Observatory]] image of [[Cygnus X-1]], which was the first strong black hole candidate discovered]]

[[X-ray binaries]] are binary systems that emit a majority of their radiation in the [[X-ray]] part of the [[electromagnetic spectrum]]. These X-ray emissions result when a compact object accretes matter from an ordinary star.<ref>{{Cite journal |last1=Schatz |first1=H. |last2=Rehm |first2=K.E. |title=X-Ray Binaries |journal=Nuclear Physics A |date=2006 |volume=777 |pages=601–622 |doi=10.1016/j.nuclphysa.2005.05.200 |arxiv=astro-ph/0607624 |bibcode=2006NuPhA.777..601S }}</ref> The presence of an ordinary star in such a system provides an opportunity for studying the central object and to determine if it might be a black hole. By measuring the [[orbital period]] of the binary, the distance to the binary from Earth, and the mass of the companion star, scientists can estimate the mass of the compact object.<ref>{{Cite journal |title=Masses and Luminosities of X-Ray Binaries |journal=SIM PlanetQuest: Science with the Space Interferometry Mission |last1=Quirrenbach |first1=Andreas |url=https://ntrs.nasa.gov/api/citations/20050186757/downloads/20050186757.pdf |last2=Frink |first2=Sabine |last3=Tomsick |first3=John |publisher=[[National Aeronautics and Space Administration]] | publication-date=2004-12-01 |bibcode=2002swsi.conf...33Q}}</ref> The [[Tolman-Oppenheimer-Volkoff limit]] (TOV limit) dictates the largest mass a nonrotating neutron star can be, and is estimated to be about two solar masses. While a rotating neutron star can be slightly more massive, if the compact object is much more massive than the TOV limit, it cannot be a neutron star and is generally expected to be a black hole.<ref name="CMS1999">{{Cite journal |last1=Celotti |first1=A. |last2=Miller |first2=J. C. |last3=Sciama |first3=D. W. |title=Astrophysical Evidence for the Existence of Black Holes |journal=Classical and Quantum Gravity |volume=16 |issue=12A |pages=A3–A21 |date=1999 |arxiv=astro-ph/9912186 |doi=10.1088/0264-9381/16/12A/301 |bibcode=1999CQGra..16A...3C |url=https://cds.cern.ch/record/411555/files/9912186.pdf|s2cid=17677758 |archive-date=27 July 2018 |archive-url=https://web.archive.org/web/20180727052939/https://cds.cern.ch/record/411555/files/9912186.pdf }}</ref><ref>{{Cite journal |last1=Cho |first1=Adrian |title=A Weight Limit Emerges for Neutron Stars |journal=Science |date=2018 |volume=359 |issue=6377 |pages=724–725 |doi=10.1126/science.359.6377.724 |pmid=29449468 |bibcode=2018Sci...359..724C }}</ref>

The first strong candidate for a black hole, [[Cygnus X-1]], was discovered in this way by [[Charles Thomas Bolton]],<ref name="Bolton1972">{{citation |last=Bolton |first=C. T. |title=Identification of Cygnus&nbsp;X-1 with HDE&nbsp;226868 |date=1972 |journal=[[Nature (journal)|Nature]] | volume=235 |issue=5336 |pages=271–273 |type=Letter |bibcode=1972Natur.235..271B |doi=10.1038/235271b0 |s2cid=4222070}}</ref> [[Louise Webster]], and [[Paul Murdin]]<ref name="Webster1972">{{citation |last1=Webster |first1=B. Louise |title=Cygnus&nbsp;X-1—a Spectroscopic Binary with a Heavy Companion? |date=1972 |journal=[[Nature (journal)|Nature]] | volume=235 |issue=5332 |pages=37–38 |type=Letter |bibcode=1972Natur.235...37W |doi=10.1038/235037a0 |s2cid=4195462 |last2=Murdin |first2=Paul |author-link2=Paul Murdin}}</ref> in 1972.<ref>{{cite web |last=Rolston |first=B. |date=10 November 1997 |url=http://news.utoronto.ca/bin/bulletin/nov10_97/art4.htm |archive-url=https://web.archive.org/web/20080502230214/http://news.utoronto.ca/bin/bulletin/nov10_97/art4.htm |archive-date=2 May 2008 |title=The First Black Hole |website=The bulletin |publisher=University of Toronto |access-date=11 March 2008}}</ref><ref name="Shipman1975" />  Observations of rotation broadening of the optical star reported in 1986 lead to a compact object mass estimate of 16 solar masses, with 7 solar masses as the lower bound.<ref name="CMS1999" /> In 2011, this estimate was updated to {{val|14.1|1.0|u=solar mass}} for the black hole and {{val|19.2|1.9|u=solar mass}} for the optical stellar companion.<ref>{{Cite journal |display-authors=2 |last1=Orosz |first1=Jerome A. |last2=McClintock |first2=Jeffrey E. |last3=Aufdenberg |first3=Jason P. |last4=Remillard |first4=Ronald A. |last5=Reid |first5=Mark J. |last6=Narayan |first6=Ramesh |last7=Gou |first7=Lijun |date=November 9, 2011 |title=The Mass of the Black Hole in Cygnus X-1 |journal=The Astrophysical Journal |volume=742 |issue=2 |page=84 |doi=10.1088/0004-637x/742/2/84 |arxiv=1106.3689 |bibcode=2011ApJ...742...84O |issn=0004-637X}}</ref>

[[X-ray binaries]] can be categorised as either <em>low-mass</em> or <em>high-mass</em>; This classification is based on the mass of the companion star, not the compact object itself.<ref name="lph97" /> In a class of X-ray binaries called soft X-ray transients, the companion star is of relatively low mass, allowing for more accurate estimates of the black hole mass. These systems actively emit X-rays for only several months once every 10–50 years. During the period of low X-ray emission, called quiescence, the accretion disk is extremely faint, allowing detailed observation of the companion star.<ref name="CMS1999" /> Numerous black hole candidates have been measured by this method.<ref>{{Cite journal |display-authors=2 |last1=Corral-Santana |first1=J. M. |last2=Casares |first2=J. |last3=Muñoz-Darias |first3=T. |last4=Bauer |first4=F. E. |last5=Martínez-Pais |first5=I. G. |last6=Russell |first6=D. M. |date=March 1, 2016 |title=BlackCAT: A Catalogue of Stellar-Mass Black Holes in X-Ray Transients |url=https://www.aanda.org/articles/aa/abs/2016/03/aa27130-15/aa27130-15.html |journal=Astronomy & Astrophysics |language=en |volume=587 |pages=A61 |doi=10.1051/0004-6361/201527130 |arxiv=1510.08869 |bibcode=2016A&A...587A..61C |issn=0004-6361}}</ref> Black holes are also sometimes found in binaries with other compact objects, such as [[white dwarf]]s,<ref name="lph97" /> neutron stars,<ref>{{Cite journal |last1=Broekgaarden |first1=Floor S. |last2=Berger |first2=Edo |title=Formation of the First Two Black Hole–Neutron Star Mergers (GW200115 and GW200105) from Isolated Binary Evolution |journal=The Astrophysical Journal Letters |date=2021 |volume=920 |issue=1 |pages=L13 |doi=10.3847/2041-8213/ac2832 |arxiv=2108.05763 |bibcode=2021ApJ...920L..13B |doi-access=free }}</ref><ref>{{Cite journal |display-authors=2 |last1=Chattopadhyay |first1=Debatri |last2=Stevenson |first2=Simon |last3=Broekgaarden |first3=Floor |last4=Antonini |first4=Fabio |last5=Belczynski |first5=Krzysztof |title=Modelling the Formation of the First Two Neutron Star–Black Hole Mergers, GW200105 and GW200115: Metallicity, Chirp Masses, And Merger Remnant Spins |journal=Monthly Notices of the Royal Astronomical Society |date=2022 |volume=513 |issue=4 |pages=5780–5789 |doi=10.1093/mnras/stac1283 |doi-access=free }}</ref> and other black holes.<ref>{{Cite journal |display-authors=2 |last1=Ziosi |first1=B. M. |last2=Mapelli |first2=M. |last3=Branchesi |first3=M. |last4=Tormen |first4=G. |title=Dynamics of Stellar Black Holes in Young Star Clusters with Different Metallicities – II. Black Hole-Black Hole Binaries |journal=Monthly Notices of the Royal Astronomical Society |date=2014 |volume=441 |issue=4 |pages=3703–3717 |doi=10.1093/mnras/stu824 |doi-access=free |arxiv=1404.7147 }}</ref><ref>{{Cite web |title=Sources and Types of Gravitational Waves |url=https://www.ligo.caltech.edu/page/gw-sources |access-date=26 October 2025 |website=LIGO Caltech}}</ref>

=== Galactic nuclei ===
The centre of nearly every galaxy contains a supermassive black hole.<ref>{{Cite journal |display-authors=2 |last1=Cattaneo |first1=A. |last2=Faber |first2=S. M. |last3=Binney |first3=J. |last4=Dekel |first4=A. |last5=Kormendy |first5=J. |last6=Mushotzky |first6=R. |last7=Babul |first7=A. |last8=Best |first8=P. N. |last9=Brüggen |first9=M. |last10=Fabian |first10=A. C. |last11=Frenk |first11=C. S. |last12=Khalatyan |first12=A. |last13=Netzer |first13=H. |last14=Mahdavi |first14=A. |last15=Silk |first15=J. |date=July 2009 |title=The Role of Black Holes in Galaxy Formation and Evolution |url=https://www.nature.com/articles/nature08135 |journal=Nature |language=en |volume=460 |issue=7252 |pages=213–219 |doi=10.1038/nature08135 |pmid=19587763 |arxiv=0907.1608 |bibcode=2009Natur.460..213C |issn=0028-0836}}</ref> The close observational correlation between the mass of this hole and the velocity dispersion of the host galaxy's [[galactic bulge|bulge]], known as the [[M–sigma relation]], strongly suggests a connection between the formation of the black hole and that of the galaxy itself.<ref name="King">{{cite journal |last=King |first=A. |title=Black Holes, Galaxy Formation, And the MBH-σ Relation |journal=The Astrophysical Journal Letters |volume=596 |issue=1 |pages=27–29 |date=2003 |doi=10.1086/379143 |arxiv=astro-ph/0308342|bibcode=2003ApJ...596L..27K|s2cid=9507887 }}</ref><ref name="msigma2000">{{cite journal |title=A Fundamental Relation Between Supermassive Black Holes and Their Host Galaxies |last1=Ferrarese |first1=L. |last2=Merritt |first2=D. |author2-link=David Merritt |journal=The Astrophysical Journal Letters |volume=539 |issue=1 |pages=9–12 |date=2000 |bibcode=2000ApJ...539L...9F |doi=10.1086/312838 |arxiv=astro-ph/0006053 |s2cid=6508110}}</ref>

==== Active galactic nucleus ====
{{See also|Active galactic nucleus}}
[[File:X-RayFlare-BlackHole-MilkyWay-20140105.jpg|thumb|alt=The center of the Milky Way, with an inset X-ray image of Sagittarius A*|Detection of an unusually bright [[X-ray]] flare from Sagittarius A*, a black hole in the centre of the Milky Way galaxy on 5{{nbsp}}January 2015<ref name="NASA-20150105">{{cite web |last1=Chou |first1=Felicia |last2=Anderson |first2=Janet |last3=Watzke |first3=Megan |date=5 January 2015 |title=RELEASE 15-001—NASA's Chandra Detects Record-Breaking Outburst from Milky Way's Black Hole |url=http://www.nasa.gov/press/2015/january/nasa-s-chandra-detects-record-breaking-outburst-from-milky-way-s-black-hole/ |url-status=live |archive-url=https://web.archive.org/web/20150106100532/http://www.nasa.gov/press/2015/january/nasa-s-chandra-detects-record-breaking-outburst-from-milky-way-s-black-hole/ |archive-date=6 January 2015 |access-date=6 January 2015 |website=[[NASA]]}}</ref>]]

Astronomers use the term ''active galaxy'' to describe galaxies with unusual characteristics, such as unusual [[spectral line]] emission and very strong radio emission. Theoretical and observational studies have shown that the high levels of activity in the centers of these galaxies, regions called active galactic nuclei (AGN), may be explained by accretion onto supermassive black holes. These AGN consist of a central black hole that may be millions or billions of times more massive than the [[Sun]], a disk of [[interstellar gas]] and dust called an accretion disk, and two [[relativistic jet|jets]] perpendicular to the accretion disk.<ref>{{multiref2|{{cite book |first=J. H. |last=Krolik |date=1999 |title=Active Galactic Nuclei |publisher=Princeton University Press |isbn=978-0-691-01151-6 |at=Ch. 1.2 |url=https://books.google.com/books?id=oRK8otMiWIgC&q=Active+Galactic+Nuclei |access-date=16 October 2020 |archive-date=14 August 2021 |archive-url=https://web.archive.org/web/20210814220336/https://books.google.com/books?id=oRK8otMiWIgC&q=Active+Galactic+Nuclei |url-status=live }}|{{cite book |first1=L. S. |last1=Sparke |author-link=Linda Sparke |first2=J. S. |last2=Gallagher |date=2000 |title=Galaxies in the Universe: An Introduction |publisher=Cambridge University Press |at=Ch. 9.1 |url=https://books.google.com/books?id=N8Hngab5liQC&q=Galaxies+in+the+Universe:+An+Introduction |isbn=978-0-521-59740-1 |access-date=16 October 2020 |archive-date=22 March 2022 |archive-url=https://web.archive.org/web/20220322141933/https://books.google.com/books?id=N8Hngab5liQC&q=Galaxies+in+the+Universe%3A+An+Introduction |url-status=live }}|{{Cite journal |display-authors=2 |last1=Marconi |first1=A. |last2=Risaliti |first2=G. |last3=Gilli |first3=R. |last4=Hunt |first4=L. K. |last5=Maiolino |first5=R. |last6=Salvati |first6=M. |title=Local Supermassive Black Holes, Relics of Active Galactic Nuclei and the X-Ray Background |journal=Monthly Notices of the Royal Astronomical Society |date=2004 |volume=351 |issue=1 |pages=169–185 |doi=10.1111/j.1365-2966.2004.07765.x |arxiv=astro-ph/0311619 |bibcode=2004MNRAS.351..169M |doi-access=free }}}}</ref>

Although supermassive black holes are expected to be found in most AGN, only some galaxies' nuclei have been more carefully studied in attempts to both identify and measure the actual masses of the central supermassive black hole candidates. Some of the most notable galaxies with supermassive black hole candidates include the [[Andromeda Galaxy]], [[Messier 32]], [[Messier 87]], the [[Sombrero Galaxy]], and the Milky Way itself.<ref name="kormendyrichstone1995">{{cite journal |first1=J. |last1=Kormendy |first2=D. |last2=Richstone |title=Inward Bound—The Search For Supermassive Black Holes In Galactic Nuclei |journal=Annual Review of Astronomy and Astrophysics |date=1995 |volume=33 |issue=1 |pages=581–624 |bibcode=1995ARA&A..33..581K |doi=10.1146/annurev.aa.33.090195.003053}}</ref><ref>{{Cite journal |last1=Melia |first1=Fulvio |last2=Falcke |first2=Heino |title=The Supermassive Black Hole at the Galactic Center |journal=Annual Review of Astronomy and Astrophysics |date=2001 |volume=39 |pages=309–352 |doi=10.1146/annurev.astro.39.1.309 |arxiv=astro-ph/0106162 |bibcode=2001ARA&A..39..309M }}</ref>

=== Microlensing ===
[[File:Gravitational microlensing by black hole - cropped.jpg|thumb|alt=A diagram of gravitational microlensing: A foreground black hole warps light from a background star, creating two images of the star. The light then travels to Earth-based telescopes, where the two images cannot be resolved and appear solely as a single brightened star.|The intense gravitational field of a foreground black hole acts like a powerful lens, distorting and brightening the image of a background star.]]
Another way black holes can be detected is through observation of effects caused by their strong gravitational field. One such effect is [[gravitational lensing]]: the deformation of spacetime around a massive object causes light rays to be deflected, making objects behind them appear distorted.<ref>{{Cite journal |last1=Wambsganss |first1=Joachim |title=Gravitational Lensing in Astronomy |journal=Living Reviews in Relativity |date=1998 |volume=1 |issue=1 |article-number=12 |doi=10.12942/lrr-1998-12 |pmid=28937183 |pmc=5567250 |arxiv=astro-ph/9812021 |bibcode=1998LRR.....1...12W |doi-access=free }}</ref> When the lensing object is a black hole, this effect can be strong enough to create multiple images of a star or other luminous source.<ref name="bm05">{{Cite journal |last1=Bozza |first1=V. |last2=Mancini |first2=L. |title=Gravitational Lensing of Stars in the Central Arcsecond of Our Galaxy |journal=The Astrophysical Journal |date=2005 |volume=627 |issue=2 |pages=790–802 |doi=10.1086/430664 |arxiv=astro-ph/0503664 |bibcode=2005ApJ...627..790B }}</ref> However, the distance between the lensed images may be too small for contemporary telescopes to [[angular resolution|resolve]]—this phenomenon is called [[microlensing]].<ref>{{Cite book |last1=Wambsganss |first1=J. |title=Gravitational Lensing: Strong, Weak and Micro |chapter=Gravitational Microlensing |series=Saas-Fee Advanced Courses |date=2006 |volume=33 |pages=453–540 |doi=10.1007/978-3-540-30310-7_4 |arxiv=astro-ph/0604278 |isbn=978-3-540-30309-1 }}</ref> Instead of seeing two images of a lensed star, astronomers see the star brighten slightly as the black hole moves towards the [[line of sight]] between the star and Earth and then return to its normal luminosity as the black hole moves away.<ref>{{Cite journal |last1=Mao |first1=Shude |title=Astrophysical Applications of Gravitational Microlensing |journal=Research in Astronomy and Astrophysics |date=2012 |volume=12 |issue=8 |pages=947–972 |doi=10.1088/1674-4527/12/8/005 |arxiv=1207.3720 |bibcode=2012RAA....12..947M }}</ref> The first three candidate black holes detected in this way were found around the turn of the millennium.<ref>{{cite journal |display-authors=2 |last1=Bennett |first1=D. P. |last2=Becker |first2=A. C. |last3=Quinn |first3=J. L. |last4=Tomaney |first4=A. B. |last5=Alcock |first5=C. |last6=Allsman |first6=R. A. |last7=Alves |first7=D. R. |last8=Axelrod |first8=T. S. |last9=Calitz |first9=J. J. |last10=Cook |first10=K. H. |last11=Drake |first11=A. J. |last12=Fragile |first12=P. C. |last13=Freeman |first13=K. C. |last14=Geha |first14=M. |last15=Griest |first15=K. |date=1 November 2002 |title=Gravitational Microlensing Events Due to Stellar-Mass Black Holes |url=https://ui.adsabs.harvard.edu/abs/2002ApJ...579..639B/abstract |journal=The Astrophysical Journal |volume=579 |issue=2 |pages=639–659 |doi=10.1086/342225 |arxiv=astro-ph/0109467 |bibcode=2002ApJ...579..639B |issn=0004-637X}}</ref><ref>{{cite journal |display-authors=2 |last1=Mao |first1=Shude |last2=Smith |first2=Martin C. |last3=Woźniak |first3=P. |last4=Udalski |first4=A. |last5=Szymański |first5=M. |last6=Kubiak |first6=M. |last7=Pietrzyński |first7=G. |last8=Soszyński |first8=I. |last9=Żebruń |first9=K. |date=1 January 2002 |title=Optical Gravitational Lensing Experiment OGLE-1999-BUL-32: The Longest Ever Microlensing Event – Evidence for a Stellar Mass Black Hole? |journal=Monthly Notices of the Royal Astronomical Society |volume=329 |issue=2 |pages=349–354 |doi=10.1046/j.1365-8711.2002.04986.x |doi-access=free |arxiv=astro-ph/0108312 |bibcode=2002MNRAS.329..349M |issn=0035-8711}}</ref> In January 2022, astronomers reported the first confirmed detection of an ''isolated'' stellar black hole—a black hole with no binary partner—and its mass; The black hole was found via detection of microlensing by the [[Hubble Space Telescope]].<ref name="Sahu">{{cite journal |arxiv=2201.13296 |last1=Sahu |first1=K. C. |title=An Isolated Stellar-Mass Black Hole Detected Through Astrometric Microlensing |journal=Astrophysical Journal|date=2022|volume=933 |issue=1 |page=83 |doi=10.3847/1538-4357/ac739e |bibcode=2022ApJ...933...83S |s2cid=246430448 |doi-access=free }}</ref><ref>{{Cite journal |last1=Lam |first1=Casey Y. |last2=Lu |first2=Jessica R. |date=October 1, 2023 |title=A Reanalysis of the Isolated Black Hole Candidate OGLE-2011-BLG-0462/MOA-2011-BLG-191 |journal=The Astrophysical Journal |volume=955 |issue=2 |pages=116 |doi=10.3847/1538-4357/aced4a |doi-access=free |arxiv=2308.03302 |bibcode=2023ApJ...955..116L |issn=0004-637X}}</ref>

== Areas of investigation ==
=== Information loss paradox ===
{{Main|Black hole information paradox}}

{{unsolved|physics|Is physical information lost in black holes?}}

According to the no-hair theorem, a black hole is defined by only three parameters: its mass, charge, and angular momentum. This seems to mean that all other information about the matter that went into forming the black hole is lost, as there is no way to determine anything about the black hole from outside other than those three parameters. When black holes were thought to persist forever, this information loss was not problematic, as the information can be thought of as existing inside the black hole. However, black holes slowly evaporate by emitting Hawking radiation. This radiation does not appear to carry any additional information about the matter that formed the black hole, meaning that this information is seemingly gone forever. This is called the [[black hole information paradox]].<ref name="PlayDice000">{{cite web |title=Does God Play Dice? |first=S. W. |last=Hawking |url=http://www.hawking.org.uk/does-god-play-dice.html |website=www.hawking.org.uk |access-date=14 March 2009 |archive-url=https://web.archive.org/web/20120111012413/http://www.hawking.org.uk/does-god-play-dice.html |archive-date=11 January 2012 }}</ref><ref name="math_ucr_edu">{{cite web |url=http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/info_loss.html |title=The Black Hole Information Loss Problem |website=Usenet Physics FAQ |last=Anderson |first=Warren G. |date=1996 |access-date=24 March 2009 |archive-url=https://web.archive.org/web/20090122223839/http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/info_loss.html |archive-date=22 January 2009}}</ref><ref name="Preskill1994">{{cite conference |last=Preskill |first=J. |author-link1=John Preskill |url=http://www.theory.caltech.edu/~preskill/talks/blackholes.pdf |title=Black Holes and Information: A Crisis in Quantum Physics |date=21 October 1994 |conference=Caltech Theory Seminar |archive-url=https://web.archive.org/web/20080518054438/http://www.theory.caltech.edu/~preskill/talks/blackholes.pdf |archive-date=18 May 2008 |access-date=17 May 2009 }}</ref> Theoretical studies analysing the paradox have led to both further paradoxes and new ideas about the intersection of quantum mechanics and general relativity. While there is no consensus on the resolution of the paradox, work on the problem is expected to be important for a theory of [[quantum gravity]].<ref>{{Cite journal |last=Raju |first=Suvrat |date=January 2022 |title=Lessons from the Information Paradox |url=https://linkinghub.elsevier.com/retrieve/pii/S0370157321003720 |journal=Physics Reports |language=en |volume=943 |pages=1–80 |doi=10.1016/j.physrep.2021.10.001 |arxiv=2012.05770 |bibcode=2022PhR...943....1R }}</ref>{{rp|126}}

=== Supermassive black holes in the early universe ===
[[File:High-Redshift Quasar and Companion Galaxy (Illustration) (2020-51-4755-Image).png|thumb |alt=Two spiral galaxies, one of which has a very bright center |Two galaxies from the first billion years after the Big Bang. The galaxy on the left hosts a luminous quasar at its center.]]
Observations of faraway galaxies have found that ultraluminous quasars, powered by supermassive black holes, existed in the early universe as far as redshift <math>z\ge7</math>.<ref>{{Cite journal |display-authors=2 |last1=Wang |first1=Feige |last2=Yang |first2=Jinyi |last3=Fan |first3=Xiaohui |last4=Hennawi |first4=Joseph F. |last5=Barth |first5=Aaron J. |last6=Banados |first6=Eduardo |last7=Bian |first7=Fuyan |last8=Boutsia |first8=Konstantina |last9=Connor |first9=Thomas |last10=Davies |first10=Frederick B. |last11=Decarli |first11=Roberto |last12=Eilers |first12=Anna-Christina |last13=Farina |first13=Emanuele Paolo |last14=Green |first14=Richard |last15=Jiang |first15=Linhua |last16=Li |first16=Jiang-Tao |last17=Mazzucchelli |first17=Chiara |last18=Nanni |first18=Riccardo |last19=Schindler |first19=Jan-Torge |last20=Venemans |first20=Bram |last21=Walter |first21=Fabian |last22=Wu |first22=Xue-Bing |last23=Yue |first23=Minghao |title=A Luminous Quasar at Redshift 7.642 |journal=The Astrophysical Journal Letters |date=2021 |volume=907 |issue=1 |pages=L1 |doi=10.3847/2041-8213/abd8c6 |arxiv=2101.03179 |bibcode=2021ApJ...907L...1W |doi-access=free }}</ref> These black holes have been assumed to be the products of the gravitational collapse of large [[population III star]]s.<ref>{{Cite journal |last1=Trenti |first1=M. |last2=Stiavelli |first2=M. |title=Distribution of the Very First Population III Stars and Their Relation to Bright ''z'' ≈ 6 Quasars |journal=The Astrophysical Journal |date=2007 |volume=667 |issue=1 |pages=38–48 |doi=10.1086/520502 |arxiv=0705.3843 |bibcode=2007ApJ...667...38T }}</ref><ref>{{Cite journal |last1=Singh |first1=Jasbir |last2=Monaco |first2=Pierluigi |last3=Tan |first3=Jonathan C. |title=The Formation of Supermassive Black Holes from Population III.1 Seeds. II. Evolution to the Local Universe |journal=Monthly Notices of the Royal Astronomical Society |date=2023 |volume=525 |pages=969–982 |doi=10.1093/mnras/stad2346 |doi-access=free }}</ref> However, these stellar remnants were not massive enough to produce the quasars observed at early times without accreting beyond the Eddington limit, the theoretical maximum rate of black hole accretion.<ref name="sb19">{{Cite journal |last1=Smith |first1=Aaron |last2=Bromm |first2=Volker |title=Supermassive Black Holes in the Early Universe |journal=Contemporary Physics |date=2019 |volume=60 |issue=2 |pages=111–126 |doi=10.1080/00107514.2019.1615715 |arxiv=1904.12890 |bibcode=2019ConPh..60..111S }}</ref><ref>{{Cite journal |display-authors=2 |last1=Jeon |first1=Myoungwon |last2=Pawlik |first2=Andreas H. |last3=Bromm |first3=Volker |last4=Milosavljević |first4=Miloš |title=Radiative Feedback from High-Mass X-Ray Binaries on the Formation of the First Galaxies and Early Reionization |journal=Monthly Notices of the Royal Astronomical Society |date=2014 |volume=440 |issue=4 |pages=3778–3796 |doi=10.1093/mnras/stu444 |doi-access=free }}</ref>

Physicists have suggested a variety of different mechanisms by which these supermassive black holes may have formed. It has been proposed that smaller black holes may have also undergone mergers to produce the observed supermassive black holes.<ref>{{Cite journal |last1=Miralda-Escudé |first1=Jaiyul Yoo Jordi |last2=Miralda-Escudé |first2=Jordi |title=Formation of the Black Holes in the Highest Redshift Quasars |journal=The Astrophysical Journal |date=2004 |volume=614 |issue=1 |pages=L25–L28 |doi=10.1086/425416 |arxiv=astro-ph/0406217 |bibcode=2004ApJ...614L..25Y }}</ref><ref>{{Cite journal |last1=Trakhtenbrot |first1=Benny |title=What Do Observations Tell Us About the Highest-Redshift Supermassive Black Holes? |journal=Proceedings of the International Astronomical Union |date=2019 |volume=15 |pages=261–275 |doi=10.1017/S1743921320003087 |arxiv=2002.00972 }}</ref> It is also possible that they were seeded by [[direct-collapse black hole]]s, in which a large cloud of hot gas avoids fragmentation that would lead to multiple stars, due to low angular momentum or heating from a nearby galaxy. Given the right circumstances, a single supermassive star forms and collapses directly into a black hole without undergoing typical [[stellar evolution]].<ref>{{Cite journal |last1=Mayer |first1=Lucio |last2=Bonoli |first2=Silvia |title=The Route to Massive Black Hole Formation via Merger-Driven Direct Collapse: A Review |journal=Reports on Progress in Physics |date=2019 |volume=82 |issue=1 |page=016901 |doi=10.1088/1361-6633/aad6a5 |pmid=30057369 |arxiv=1803.06391 |bibcode=2019RPPh...82a6901M }}</ref><ref>{{Cite journal |display-authors=2 |last1=Agarwal |first1=Bhaskar |last2=Dalla Vecchia |first2=Claudio |last3=Johnson |first3=Jarrett L. |last4=Khochfar |first4=Sadegh |last5=Paardekooper |first5=Jan-Pieter |title=The First Billion Years Project: Birthplaces of Direct Collapse Black Holes |journal=Monthly Notices of the Royal Astronomical Society |date=2014 |volume=443 |pages=648–657 |doi=10.1093/mnras/stu1112 |doi-access=free }}</ref> Additionally, these supermassive black holes in the early universe may be high-mass primordial black holes, which could have accreted further matter in the centers of galaxies.<ref>{{Cite journal |display-authors=2 |last1=Shinohara |first1=Takumi |last2=He |first2=Wanqiu |last3=Matsuoka |first3=Yoshiki |last4=Nagao |first4=Tohru |last5=Suyama |first5=Teruaki |last6=Takahashi |first6=Tomo |title=Supermassive Primordial Black Holes: A View from Clustering of Quasars at <math>z\sim6</math> |journal=Physical Review D |date=2023 |volume=108 |issue=6 |article-number=063510 |doi=10.1103/PhysRevD.108.063510}}</ref> Finally, certain mechanisms allow black holes to grow faster than the theoretical Eddington limit, such as dense gas in the accretion disk limiting outward radiation pressure that prevents the black hole from accreting.<ref name="sb19" /><ref>{{Cite book |last1=Mayer |first1=Lucio |title=Formation of the First Black Holes |chapter=Super-Eddington accretion; flow regimes and conditions in high-z galaxies |date=2019 |pages=195–222 |doi=10.1142/9789813227958_0011 |arxiv=1807.06243 |isbn=978-981-322-794-1 }}</ref> However, the formation of bipolar jets prevent super-Eddington rates.<ref name="Regan" />

===Alternatives to black holes===
{{See also|Exotic star}}
While there is a strong case for supermassive black holes,<ref>{{Cite journal |last1=Maoz |first1=Eyal |title=Dynamical Constraints on Alternatives to Supermassive Black Holes in Galactic Nuclei |journal=The Astrophysical Journal |date=1998 |volume=494 |issue=2 |pages=L181–L184 |doi=10.1086/311194 |arxiv=astro-ph/9710309 |bibcode=1998ApJ...494L.181M }}</ref><ref>{{Cite journal |last1=Miller |first1=M. Coleman |title=Constraints on Alternatives to Supermassive Black Holes |journal=Monthly Notices of the Royal Astronomical Society: Letters |date=2006 |volume=367 |issue=1 |pages=L32–L36 |doi=10.1111/j.1745-3933.2006.00135.x |arxiv=astro-ph/0512194 |bibcode=2006MNRAS.367L..32M |doi-access=free }}</ref> the dividing line between lighter black holes and neutron stars relies on theories of extremely dense matter. Direct observational tests are not available: objects observed to have mass higher than the predictions for neutron stars are assumed to be black holes. Recent evidence from gravitational wave events suggests modifications of these theories may be needed.<ref name="Vink-2021"/> New exotic [[Phase (matter)|phases of matter]] could allow other kinds of massive objects.<ref name="CMS1999" /> [[Quark star]]s would be made up of [[quark matter]] and supported by quark degeneracy pressure, a form of degeneracy pressure even stronger than neutron degeneracy pressure. This would halt gravitational collapse at a higher mass than for a neutron star.<ref>{{cite journal |last1=Kovacs |first1=Z. |last2=Cheng |first2=K. S. |last3=Harko |first3=T. |title=Can Stellar Mass Black Holes Be Quark Stars? |journal=[[Monthly Notices of the Royal Astronomical Society]] | date=2009 |volume=400 |issue=3 |pages=1632–1642 |doi=10.1111/j.1365-2966.2009.15571.x |doi-access=free |arxiv=0908.2672 |bibcode=2009MNRAS.400.1632K |s2cid=18263809}}</ref><ref>{{Cite journal |last1=Sotani |first1=Hajime |last2=Kohri |first2=Kazunori |last3=Harada |first3=Tomohiro |title=Restricting Quark Matter Models by Gravitational Wave Observation |journal=Physical Review D |date=2004 |volume=69 |issue=8 |article-number=084008 |doi=10.1103/PhysRevD.69.084008 |arxiv=gr-qc/0310079 |bibcode=2004PhRvD..69h4008S }}</ref> Even stronger stars called [[electroweak star]]s would convert quarks in their cores into [[lepton]]s, providing additional pressure to stop the star from collapsing.<ref name="bonkowsky25">{{Cite web |title=Between Neutron Stars and Black Holes |url=https://www.thecolumbiasciencereview.com/online-articles/between-neutron-stars-and-black-holes |last=Bonkowsky |first=Charles |date=2025-01-05 |access-date=2025-12-06 |website=Columbia Science Review}}</ref><ref>{{Cite journal |display-authors=2 |last1=Dai |first1=De-Chang |last2=Lue |first2=Arthur |last3=Starkman |first3=Glenn |last4=Stojkovic |first4=Dejan |title=Electroweak Stars: How Nature May Capitalize on the Standard Model's Ultimate Fuel |journal=Journal of Cosmology and Astroparticle Physics |date=2010 |issue=12 |page=004 |doi=10.1088/1475-7516/2010/12/004 |arxiv=0912.0520 |bibcode=2010JCAP...12..004D }}</ref> If, as some extensions of the [[Standard Model]] posit, [[quark]]s and [[lepton]]s are made up of the even-smaller fundamental particles called [[preon]]s, a very compact star could be supported by preon degeneracy pressure.<ref>{{cite journal |last1=Hansson |first1=J. |last2=Sandin |first2=F. |title=Preon Stars: A New Class of Cosmic Compact Objects |journal=Physics Letters B |volume=616 |issue=1–2 |pages=1–7 |date=2005 |doi=10.1016/j.physletb.2005.04.034 |arxiv=astro-ph/0410417 |bibcode=2005PhLB..616....1H |s2cid=119063004}}</ref> While none of these hypothetical models can explain all of the observations of stellar black hole candidates, a [[Q star]] is the only alternative which could significantly exceed the mass limit for neutron stars and thus provide an alternative for supermassive black holes.<ref name="CMS1999" />{{rp|12}}

A few theoretical objects have been conjectured to match observations of astronomical black hole candidates identically or near-identically, but which function via a different mechanism.<ref name="Murk2023">{{cite journal |last=Murk |first=Sebastian |title=Nomen Non Est Omen: Why It Is Too Soon to Identify Ultra-Compact Objects as Black Holes |journal=International Journal of Modern Physics D |year=2023 |volume=32 |issue=14 |pages=2342012–2342235 |article-number=2342012 |doi=10.1142/S0218271823420129 |arxiv=2210.03750 |bibcode=2023IJMPD..3242012M |s2cid=252781040}}</ref> A [[dark energy star]] would convert infalling matter into [[vacuum energy]]; This vacuum energy would be much larger than the vacuum energy of outside space, exerting outwards pressure and preventing a singularity from forming.<ref>{{Cite journal |last1=Bagheri Tudeshki |first1=A. |last2=Bordbar |first2=G.H. |last3=Eslam Panah |first3=B. |title=Dark Energy Star in Gravity's Rainbow |journal=Physics Letters B |date=2022 |volume=835 |article-number=137523 |doi=10.1016/j.physletb.2022.137523 |arxiv=2208.07063 |bibcode=2022PhLB..83537523B }}</ref><ref>{{cite journal |last1=Ball |first1=Philip |title=Black Holes 'Do Not Exist' |journal=Nature |date=31 March 2005 |doi=10.1038/news050328-8}}</ref> A [[black star (semiclassical gravity)|black star]] would be gravitationally collapsing slowly enough that quantum effects would keep it just on the cusp of fully collapsing into a black hole.<ref>{{Cite journal |display-authors=2 |last1=Barceló |first1=Carlos |last2=Liberati |first2=Stefano |last3=Sonego |first3=Sebastiano |last4=Visser |first4=Matt |title=Fate of Gravitational Collapse in Semiclassical Gravity |journal=Physical Review D |date=2008 |volume=77 |issue=4 |article-number=044032 |doi=10.1103/PhysRevD.77.044032 |arxiv=0712.1130 |bibcode=2008PhRvD..77d4032B }}</ref> A [[gravastar]] would consist of a very thin shell and a dark-energy interior providing outward pressure to stop the collapse into a black hole or formation of a singularity; It could even have another gravastar inside, called a 'nestar'.<ref>{{Cite journal |last1=Jampolski |first1=Daniel |last2=Rezzolla |first2=Luciano |title=Nested Solutions of Gravitational Condensate Stars |journal=Classical and Quantum Gravity |date=2024 |volume=41 |issue=6 |doi=10.1088/1361-6382/ad2317 |arxiv=2310.13946 |bibcode=2024CQGra..41f5014J }}</ref>

== In fiction ==
{{Main|Black holes in fiction}}

[[File:Interstellar black hole (no lens flare).jpg|thumb|alt=A black hole over a black background surrounded by a light orange accretion disk. The disk wraps around the top and bottom of the black hole, and across the front like a crossbar. A white, mostly-circular photon sphere is slightly inset inside the black hole's shadow.|The black hole and accretion disk used in the movie ''Interstellar'', without lens flare. Interstellar's visual effects team used relativity to visualize gravitational lensing around the black hole.<ref name="jtft15" />]]

Black holes have been portrayed in science fiction in a variety of ways. Even before the advent of the term itself, objects with characteristics of black holes appeared in stories such as the 1928 novel ''[[The Skylark of Space]]'' with its "black Sun" and the "hole in space" in the 1935 short story ''[[Starship Invincible]]''.<ref name="WestfahlBlackHoles">{{Cite book |last=Westfahl |first=Gary |title=[[Science Fiction Literature Through History: An Encyclopedia]] | date=2021 |publisher=ABC-CLIO |isbn=978-1-4408-6617-3 |pages=159–162 |language=en |chapter=Black Holes |author-link=Gary Westfahl |chapter-url=https://books.google.com/books?id=WETPEAAAQBAJ&pg=PA159}}</ref> As black holes grew to public recognition in the 1960s and 1970s, they began to be featured in films as well as novels, such as Disney's ''[[The Black Hole (film)|The Black Hole]]''.<ref name="kyle19">{{Cite magazine |date=2019-06-19 |title=Understanding Black Holes Through Science Fiction |magazine=Sci Phi Journal |last=Johnson |first=David Kyle |url=https://www.sciphijournal.org/index.php/2019/06/19/understanding-black-holes-through-science-fiction/ |access-date=2025-12-20}}</ref><ref name="rodriguezblackstar">{{Cite journal |title="Blame It on the Black Star": Black Holes in Culture |journal=IAFOR Journal of Cultural Studies |last=Rodriguez |first=Mario |url=https://www.researchgate.net/publication/376983839 |volume=8 |issue=2 |via=ResearchGate}}</ref> In the 21st century, as [[computer-generated imagery]] advanced, visual media such as the 2014 space epic [[Interstellar (film)|Interstellar]] and the 2018 science fiction film [[High Life (film)|High Life]] have incorporated relativity into their visualizations, although both used some [[artistic license]].<ref>{{Cite web |title=How 'High Life' Created a Black Hole That Looks Just Like the Historic Photo |url=https://www.inverse.com/article/55087-high-life-claire-denis-aurelien-barrau-got-black-holes-right |last=Tayag |first=Yasmin |date=2019-04-20 |access-date=2026-03-31 |website=Inverse}}</ref><ref name="jtft15" />

Authors and screenwriters have exploited the relativistic effects of black holes, particularly gravitational time dilation.<ref name="StablefordBlackHole">{{Cite book |last=Stableford |first=Brian |title=[[Science Fact and Science Fiction: An Encyclopedia]] | date=2006 |publisher=Taylor & Francis |isbn=978-0-415-97460-8 |pages=65–67 |language=en |chapter=Black Hole |author-link=Brian Stableford |chapter-url=https://books.google.com/books?id=uefwmdROKTAC&pg=PA65}}</ref> For example, ''Interstellar'' features a [[blanet|black hole planet]] with a time dilation factor of over 60,000:1,<ref name="scienceofinterstellar" />{{rp|163}} while the 1977 [[Frederik Pohl|Pohl]] novel ''[[Gateway (novel)|Gateway]]'' depicts a spaceship approaching but never crossing the event horizon of a black hole from the perspective of an outside observer due to time dilation effects.<ref name="GreenwoodBlackHoles">{{Cite book |last=Langford |first=David |title=[[The Greenwood Encyclopedia of Science Fiction and Fantasy: Themes, Works, And Wonders]] | date=2005 |publisher=Greenwood Publishing Group |isbn=978-0-313-32951-7 |editor-last=Westfahl |editor-first=Gary |editor-link=Gary Westfahl |pages=89–91 |language=en |chapter=Black Holes |author-link=David Langford |chapter-url=https://archive.org/details/greenwoodencyclo0000unse_k2b9/page/89/mode/2up}}</ref> Black holes have also been appropriated as wormholes or other methods of faster-than-light travel, such as in the 1974 [[Joe Haldeman|Haldeman]] novel ''[[The Forever War]]'', where a network of black holes is used for interstellar travel.<ref name="StablefordBlackHole" /><ref name="FraknoiBlackHoles">{{Cite web |last=Fraknoi |first=Andrew |author-link=Andrew Fraknoi |date=January 2024 |title=Science Fiction Stories with Good Astronomy & Physics: A Topical Index |url=https://astrosociety.org/file_download/inline/7b5edc23-7a89-46c1-a6b3-33a30ed4c876 |url-status=live |archive-url=https://web.archive.org/web/20240210011957/https://astrosociety.org/file_download/inline/7b5edc23-7a89-46c1-a6b3-33a30ed4c876 |archive-date=2024-02-10 |archive-format=PDF |access-date=2024-06-21 |website=[[Astronomical Society of the Pacific]] | pages=3–4 |format=PDF |edition=7.3}}</ref> Additionally, black holes can feature as hazards to spacefarers and planets: A black hole threatens a deep-space outpost in 1978 short story ''[[The Black Hole Passes]]'', and a binary black hole dangerously alters the orbit of a planet in the 2018 Netflix reboot of ''[[Lost in Space (2018)|Lost in Space]]''.<ref name="rodriguezblackstar" /><ref name="FraknoiBlackHoles" />

== Notes ==
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== References ==
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== External links ==
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{{Scholia}}
* ''[[Stanford Encyclopedia of Philosophy]]'': "[https://plato.stanford.edu/entries/spacetime-singularities/ Singularities and Black Holes]" by Erik Curiel and Peter Bokulich.
* [[ESA]]'s [https://www.esa.int/gsp/ACT/phy/Projects/Blackholes/WebGL/ Black Hole Visualization] {{Webarchive|url=https://web.archive.org/web/20190503070935/https://www.esa.int/gsp/ACT/phy/Projects/Blackholes/WebGL.html |date=3 May 2019 }}
* [https://web.archive.org/web/19980118023013/http://casa.colorado.edu/~ajsh/schw.shtml Fall Into A Black Hole] on Andrew Hamilton's website
* [https://space.geometrian.com/calcs/black-hole-params.php Black Hole Parameters] Calculator
* [https://science.nasa.gov/astrophysics/focus-areas/black-holes/stories/ Black Hole News] from NASA

=== Videos ===
* [https://www.pbs.org/video/black-hole-apocalypse-yj34qi/ ''Black Hole Apocalypse''] – documentary on [[Nova (American TV program)|NOVA]]
* [https://www.youtube.com/playlist?list=PLsPUh22kYmNBl4h0i4mI5zDflExXJMo_x Black Holes Playlist] on YouTube from ''[[PBS Space Time]]''
* [https://www.bbc.com/news/science-environment-35524440 Computer Visualisation of a Signal Detected by LIGO] – artistic visualization of gravitational waves from merging black holes
* [https://www.youtube.com/watch?v=I_88S8DWbcU Two Black Holes Merge Into One (Based Upon the Signal GW150914)] – realistic simulation of merging black holes
* [https://www.youtube.com/watch?v=crXGmeWFb9o Plunge Into A Black Hole] – 360° NASA simulation and [https://www.youtube.com/watch?v=chhcwk4-esM explanation]

{{Black holes}}
{{Relativity}}
{{String theory topics}}
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[[Category:Black holes| ]]
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[[Category:Concepts in astronomy]]
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