View source for Talk:Schwarzschild radius

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Anon  <!-- Template:Unsigned IP --><small class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/2A0C:5BC0:40:1028:694E:373B:C8BD:777|2A0C:5BC0:40:1028:694E:373B:C8BD:777]] ([[User talk:2A0C:5BC0:40:1028:694E:373B:C8BD:777#top|talk]]) 10:49, 14 December 2020 (UTC)</small> <!--Autosigned by SineBot-->

== Incorrect derivation? ==

http://scienceworld.wolfram.com/physics/SchwarzschildRadius.html
claims the derivation here is incorrect. that is it is incorrect to set the escape velocity to c the speed of light to solve for r.  On consideration, it is OBVIOUS that there is something wrong with an equation (for a finite mass) that claims v = c, isn't there? (since this is impossible.)  <small>—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/69.40.245.3|69.40.245.3]] ([[User talk:69.40.245.3|talk]]) 22:12, 23 August 2008 (UTC)</small><!-- Template:UnsignedIP --> <!--Autosigned by SineBot-->

See the note I just added above (before I noticed this comment!)
I believe wolfram is wrong.(no surprise.  I used SMP years ago.  Maxima, now...)
If I drop a rock from infinity (give it an infinitesimal shove to get it going...) then
it will accelerate towards the mass (M, at the origin), according to newton's laws, to arbitrary accuracy.  Relativistically its mass will increase (relative to a frame at the origin), but that mass cancels out (little m in my note above --  replace m by m(t) or m(x)  -- parameterized how you like - it still cancels out.)   It's more than a coincidence that the argument works.  
The exact point where that mass (relativistically) becomes infinite, is where the argument may fail - but that's because that is what it means to have an event horizon.  

Steve  <span style="font-size: smaller;" class="autosigned">—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/67.90.34.130|67.90.34.130]] ([[User talk:67.90.34.130|talk]]) 18:39, 24 March 2011 (UTC)</span><!-- Template:UnsignedIP --> <!--Autosigned by SineBot-->

== Needs square-root? ==

Shouldn't the radius =  square root ( 2GM/c^2) ???

:No, see [http://zebu.uoregon.edu/~js/glossary/schwarzschild_radius.html], [http://casa.colorado.edu/~ajsh/schwp.html], [http://scienceworld.wolfram.com/physics/SchwarzschildRadius.html], [http://www.google.com.au/search?hl=en&q=schwarzschild+radius etc.] -- [[User:Tim Starling|Tim Starling]] 04:25, Nov 18, 2004 (UTC)

::Or, more simply, using [[dimensional analysis]]:  <math>r\,</math> is in meters (<math>m\,</math>), so <math>2Gm/c^2\,</math> must be in meters also.  Let's see:
::<math>G \to N\cdot m^2/kg^2\,</math>, where <math>N\,</math> is force = mass * acceleration = <math>kg\cdot m/s^2\,</math>, so <math>G\,</math> is in units of <math>(kg \cdot m/s^2) \cdot (m^2/kg^2)\,</math>.
::<math>m/c^2\,</math> is in units of <math>kg/(m/s)^2 \to kg \cdot s^2/m^2</math>.
::So when combined <math>Gm/c^2\,</math> is in units of <math>(kg \cdot m/s^2) \cdot (m^2/kg^2) \cdot (kg \cdot s^2/m^2)</math>.
::You can see directly that units of <math>kg\,</math> and <math>s\,</math> are equal in numerator and denominator, leaving <math>m^3/m^2 \to m\,</math> (meters).
::QED.  [[User:Slowmover|Slowmover]] 20:23, 22 March 2006 (UTC)

== Meaning for non-black holes? ==

What is the physical meaning of an object's Schwarzschild radius when it is bigger than the radius? -- [[User:Myria|Myria]] 05:35, 29 December 2005 (UTC)

It means that this object is not a black hole. For an object to be a black hole, its mass needs to be concentrated in a radius less than its Schwarzschild radius. The same holds also for part of the object, so in theory it's possible that the whole object is not a black hole, but its inner part is a black hole.
This subject is important to define the moment when a collapsing star becomes a black hole. This transition happens when its mass is concentrated in a radius that is equal to its Schwarzschild radius.

I'm not exactly where to put it, but when reading this article, it took me a while to figure out that a plain-English definition of the Schwartzchild radius makes more sense.  The Schwartzchild radius is the radius for a given mass where, if that mass could be compressed to fit within that radius, no force could stop it from continuing to collapse into a singularity.  Wouldn't it be nice to put such a definition in the article?  Problem is that I'm not even remotely a physicist so I don't want to make the change myself.--[[User:MikeGinny|MikeGinny]] 04:57, 30 June 2006 (UTC)
:Giving this some thought. -- [[User:Slowmover|Slowmover]] 19:34, 30 June 2006 (UTC)
:Singularities are non-physical and normally this should be enough to dismiss models where this is a consequence. I've done Python simulations on mass with emergent space-time and the source particles always end up moving to the horizon - their time vectors pointing outwards. This suggests that the volume formula for space-time is wrong - it should be the surface of a 3-sphere. The radius should be defined as the point where a particle falling in from infinity reaches "c". [[Special:Contributions/65.181.12.102|65.181.12.102]] ([[User talk:65.181.12.102|talk]]) 12:44, 16 December 2024 (UTC)

"An object smaller than its Schwarzschild radius is called a black hole" ... ok, physics newb here, but does this mean that the universe was technically a black hole in the early stages of the big bang, or did the SR scale with the expansion of the universe? [[User:Snaxalotl|Snaxalotl]] ([[User talk:Snaxalotl|talk]]) 18:32, 7 June 2009 (UTC)snaxalotl

:: I think that one useful way to look at it is this: If you take an object with a particular mass, it has a certain amount of gravity, all of which has to exit through its surface. If you then squish the object into a smaller volume, the intensity of the gravitational field at the surface increases, and when you increase this [[surface gravity]], you increase the [[escape velocity]], the speed at which somethng has to be thrown with at the surface to have a chance of completely escaping. For a given mass M, the r=2M radius tells us how compact the material would have to be in order for this surface escape velocity to reach the critical situation of being equal to the nominal speed of light. [[John Michell]] did the calculations for this back in the Eighteenth Century, but when [[Isaac Newton]]'s original ideas about light took a hammering, the idea became unfashionable and dropped out of sight until [[Karl Schwarzchild]] brought it back, more unambigiuously, in the context of [[Einstein]]'s [[general theory of relativity]], in the early Twentieth Century. [[User:ErkDemon|ErkDemon]] 15:59, 29 December 2006 (UTC)

::: That is no answer to Snaxalotl's question: Was the universe a black hole in its early stages? [[Special:Contributions/145.97.222.84|145.97.222.84]] ([[User talk:145.97.222.84|talk]]) 17:39, 15 January 2012 (UTC)

== Gravitational versus Schwarzchild radius ==

I added a link to the hyperphysics sight because it distinguishes between a gravitational radius and a Scwarzschild radius. The distinction is an important one even though it is quite common to confuse the two.[[User:Lucretius|Lucretius]] 07:53, 15 January 2006 (UTC)

I subsequently removed the link because 'gravitaional radius' and 'Schwarzschild radius' are considered synonymous by the great majority of the scientific community.[[User:Lucretius|Lucretius]] 23:50, 15 January 2006 (UTC)

== Low density black hole ==

below are the calculations for the mass and radius of a black hole with the density of water. The resulting mass is 135 million times the mass of the Sun. The radius is 400 million kilometres.

<math>\begin{align}

&\rho=\frac{m}{\frac{4}{3}*\pi*r^3}\\ &\frac{m}{\left(\frac{2Gm}{c^2}\right)^3*\frac{4}{3}*\pi}=1000Kg/M^3\\ &\frac{m}{\frac{8G^3m^3}{c^6}*\frac{4\pi}{3} }=1000Kg/M^3\\ &\frac{3mc^6}{32*\pi*m^3G^3}=1000Kg/M^3\\ &3c^6=32000*\pi*m^2G^3*Kg/M^3\\ &m=\sqrt{\frac{3c^6}{32000*\pi*G^3*Kg/M^3} }=\frac{c^3/100}{\sqrt{3.2/3*\pi*G^3*Kg/M^3} }\\ &m\approx\frac{2.7*10^{23}M^3/\text{sec}^3}{\sqrt{10/3*3*10^{-31}M^9*\text{sec}^{-6}*Kg^{-3}*Kg/M^3} } = \frac{2.7*10^{27}M^3/\text{sec}^3}{\sqrt{10*10^{-31}M^6/\text{sec}^6*Kg^{-2} } }\\ &m\approx\frac{2.7*10^{23} }{10^{-15} }Kg=2.7*10^{38}Kg\\ &r=\frac{2Gm}{c^2}=4*10^8M \end{align}</math>

:That is the density of an object that ''perfectly fits'' its Schwarzschild radius. Pity that, once the object fits the object it will collapse into a singularity of infinite density. From the article: ''The Schwarzschild radius is the radius for a given mass where, if that mass could be compressed to fit within that radius, no known force or degeneracy pressure could stop it from continuing to collapse into a [[gravitational singularity]]'' -- which according to [[General Relativity]] means it will reach [[Black hole#Singularity at a single point|infinite density]].
: I'm not sure about what you wanted to prove. --[[User:Badpazzword|badpazzword]] ([[User talk:Badpazzword|talk]]) 08:25, 29 March 2008 (UTC)
: I think the point here is only that the density claimed is the average density for everything inside the Schwarzschild radius. A nerd fact for people who like trivia.  <small><span class="autosigned">—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Snaxalotl|Snaxalotl]] ([[User talk:Snaxalotl|talk]] • [[Special:Contributions/Snaxalotl|contribs]]) 18:25, 7 June 2009 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot-->

==Great Job on the Article==

I just wanted to let the editors of this article know this article's far better than it was before; I didn't have a good idea of the Schwarzchild radius earlier, but it's clear now. This seems to be applicable to a lot of the physics articles in particular. Just wanted to point it out- thanks a lot for your contributions! [[User:Robinson0120|Robinson0120]] 01:47, 17 January 2007 (UTC)

== Removed incorrect claim ==

I removed this sentence:

:The Schwarzschild radius of a sphere with a uniform density equal to the [[critical density]] is equal to the radius of the [[visible universe]].

because it's not true--the Schwarzschild radius in this case is about 250 Gly, and the radius of the visible universe is about 50 Gly. There's certainly a meaningful relationship here, but it's not quite so simple. (And I'm not sure exactly what it is.) -- [[User:BenRG|BenRG]] 16:11, 26 March 2007 (UTC)

== Underlying symmetry? ==

From the article:
"Note that although the result is correct, general relativity must be used to properly derive the Schwarzschild radius. Some consider it to be only a coincidence that Newtonian physics produces the same result, yet this may be an indication of a deeper underlying symmetry in nature."

The first sentence and the first half of the second sentence are my own contribution from a while back.  However, someone seems to have mangled the message by using the much weaker phrase, "Some consider it..." and the highly questionable, "yet this may be an indication of a deeper underlying symmetry in nature."  I won't blindly revert it to, "It is only a coincidence that Newtonian physics produces the same result," but I'm quite skeptical about this "underlying symmetry" they're referring to.  Newtonian physics is an ''approximation'', plain and simple.  Saying there's a symmetry between general relativity and Newtonian physics is like saying there is a symmetry between cars and engines.  Cars encompass engines-- they're not on equal footing.  You can compare different models of cars, just as you can compare general relativity to less reputable theories.  If someone knows what this underlying symmetry is, I'd love to hear about it.  Otherwise, I'll go ahead and revert that sentence to its much clearer form.--[[User:134.173.200.14|134.173.200.14]] 20:13, 3 April 2007 (UTC)

== Rotating objects ==

Is it possibly so that if an objects rotates fast you could puch some more mass within the S-radius without the object collapsing? (As Schwarzschild is, as I understand, a solution for the non-rotating case.)If so the first paragraph is not entirely correct. -- [[User:Agge1000|Agge1000]] ([[User talk:Agge1000|talk]]) 18:44, 16 November 2007 (UTC)

how about "the size of a finger nail."? finger tip?  <small>—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/69.40.245.3|69.40.245.3]] ([[User talk:69.40.245.3|talk]]) 22:14, 23 August 2008 (UTC)</small><!-- Template:UnsignedIP --> <!--Autosigned by SineBot-->

== 9 mm Walnut? ==

Quote from the article:
:while the Earth's is only about 9 mm, the size of a walnut.
Most walnuts I have known are quite a bit larger than 9 mm. Perhaps peanut would be more appropriate. --[[Special:Contributions/66.92.218.124|66.92.218.124]] ([[User talk:66.92.218.124|talk]]) 19:28, 22 May 2008 (UTC)

A peanut would be the right size, but the wrong shape. A hazelnut would be a better nut comparison though these can still be significantly larger than 9mm. However if we are considering legumes, I would suggest that chickpeas display more of the correct characteristics.  <small>—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/193.129.242.5|193.129.242.5]] ([[User talk:193.129.242.5|talk]]) 09:54, 13 June 2008 (UTC)</small><!-- Template:UnsignedIP --> <!--Autosigned by SineBot-->

It's a 9mm radius, not a diameter, so I don't think a walnut is far off.  <span style="font-size: smaller;" class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/138.16.19.174|138.16.19.174]] ([[User talk:138.16.19.174|talk]]) 23:45, 13 October 2013 (UTC)</span><!-- Template:Unsigned IP --> <!--Autosigned by SineBot-->

:As of 12/26/2014 it reads "9 mm, the size of a peanut." This is wrong.  First, a peanut contains between 2-4 seeds, and is quite a bit larger than 1.8 cm. Second, the article isn't clear if it is referring to a peanut or a peanut seed (my guess is it means peanut seed). Third, "size" can be interpreted as volume, and the peanut seed is NOT round, so the volume of a seed with a given semi-major axis compared to a ball with that diameter will be quite a bit smaller. It is a really bad comparison, imho. I don't understand why ANY comparison is necessary, simply say a its the size of a small ball of diameter about 1.8 cm or 0.7 inches. Or are we attempting to inform children who don't know what a centimeter (or inch) is (or don't understand fractions)??[[User:Abitslow|Abitslow]] ([[User talk:Abitslow|talk]]) 16:56, 26 December 2014 (UTC)


::|--------------|
That's the size of an Earth-mass black hole.

Now, your computer screen might be smaller or bigger than mine, but I've noticed that as long as they're modern screens, bigger screens tend to show more things rather than bigger things. But if you don't trust that size, find a penny. US pennies have a diameter of 19 mm, which is only about 6% bigger than the Earth hole's 18 mm event horizon. And as you can tell from where I said "19 mm," I actually ''measured'' the penny, rather than just guessing. [[Special:Contributions/50.5.96.209|50.5.96.209]] ([[User talk:50.5.96.209|talk]]) 22:07, 16 May 2017 (UTC)

== A metric for gravitational mass ==

{{float-right-begin}}
{| style="border:1px solid gray; border-collapse:collapse" cellpadding="2" cellspacing="0"
|-  style="border-bottom: 1px solid gray"
!
! align="center" | <math>r_s</math>
|-
| [[Sun]]     ||align="right" | 2953.2500765 m
|-
| [[Mercury (planet)|Mercury]] ||align="right" | 0.49028 mm
|-
| [[Venus]]   ||align="right" | 7.22909 mm
|-
| [[Earth]]   ||align="right" | 8.870056078 mm
|-
| [[Mars]]    ||align="right" | 0.95305 mm
|-
| [[Jupiter]] ||align="right" | 2.81915558 m
|-
| [[Saturn]]  ||align="right" | 0.84408275 m
|-
| [[Uranus]]  ||align="right" | 0.1289325 m
|-
| [[Neptune]] ||align="right" | 0.1521333 m
|}
{{float-right-end}}

The [[International System of Units]] (SI) has a unique unit for inertial mass (the [[kilogram]]) and a unique unit for energy (the [[Joule]]), but it does not have a unique unit for gravitational mass.  Therefore, gravitational masses are commonly listed in terms of inertial mass equivalents: for example, the mass of the earth as [http://www.google.com/search?hl=en&q=earth+mass+in+yottagrams 5974.2 yottagrams].  However, this tradition is unfortunate, and even bizarre, when one considers that there is no known way to measure the inertial mass of a planet sized object.

The masses of planets and stars are currently estimated by first measuring their gravity, and then using G in Newton's theory of gravity to estimate the inertial mass.  In fact, the inertial masses of the sun and planets have never been directly measured.  The values listed in the literature are just estimates using Newton's theory, and there is no known way to prove that these estimates are correct.

See the following article:

"http://curious.astro.cornell.edu/question.php?number=452"

As an alternative, I would propose using the “standard gravitational parameter” to directly calculate the Schwarzschild radius.  The fact that c is defined exactly allows the Schwarzschild radius of a gravitating object to be determined to the same accuracy to which one knows the gravity of the object (See the table to the right: the “standard gravitational parameters” of the sun and earth are known to over 9 digits).  And using the “standard gravitational parameter” to directly calculate the Schwarzschild radius removes the unnecessary step of estimating the Newtonian inertial mass.  Furthermore, the Schwarzschild radius can be indirectly measured by measuring time dilation near the object.  So the Schwarzschild radius has the advantage of being both accurate and measurable, whereas the inertial mass is neither measurable nor accurately determinable.

Current alternatives for listing precise gravitational masses are to list mass ratios as is done in this [http://ssd.jpl.nasa.gov/?constants NASA web site,] or to list large masses in terms of their [[standard gravitational parameter]].
[[Special:Contributions/70.176.112.179|70.176.112.179]] ([[User talk:70.176.112.179|talk]]) 04:54, 19 April 2009 (UTC)

== Supermassive Black Hole at the center of the Milky Way ==

Images toward the center of the Milky Way as seen by Hubble show that there is so much galactic matter, both stars and dust, between us and the center that it is impossible to see what is at the center.  No black hole has ever been seen at the center of our galaxy, nor any galaxy.  The luminosity at the center of galaxies is so great that detail cannot be discerned.  That black holes exist at the center of galaxies is pure speculation.  [[User:My Flatley|My Flatley]] ([[User talk:My Flatley|talk]]) 18:27, 1 October 2009 (UTC)
:If you look at [[Supermassive black hole]] they discuss the evidence for such objects there, stating that there is a consensus amongst astronomers that such things do exist. Read about the evidence, and take your discussion to their talk page if not convinced.[[User:Puzl bustr|Puzl bustr]] ([[User talk:Puzl bustr|talk]]) 15:12, 6 December 2009 (UTC)

Since 10/1/09, astrophysicits and astronomers have confirmed that tere is a supermassive black hole at the center of the Milky Way Galaxy and have predicted that there is a supermassive black hole at the center of every galaxy. - Brad Watson, Miami [[Special:Contributions/71.196.121.70|71.196.121.70]] ([[User talk:71.196.121.70|talk]]) 19:51, 11 July 2011 (UTC)

== M-sigma relation ==

I noticed someone questioned the relationship between core black hole mass and the mass of the galaxy - and this is only an ''average'' relationship with much scatter, as evidenced by their example comparing Andromeda and Milky Way. I found that there is a much tighter relationship and an article [[M-sigma relation]] discussing it, and the previous work in this area, so added a ref and the wikilink. [[User:Puzl bustr|Puzl bustr]] ([[User talk:Puzl bustr|talk]]) 15:12, 6 December 2009 (UTC)

== Schwarzschild radius for the Sun ==

I found this interesting quote and would like to start a section in the article for similar size comparisons: "The Schwarzschild radius for the Sun is about two miles, 1/200,000th of its current width; for the Earth to become a black hole, it would have to be squeezed into a ball with a radius of one centimetre." --[http://www.telegraph.co.uk/science/space/7972538/Are-we-living-in-a-designer-universe.html Are we living in a designer universe?] --[[User:Thorwald|Thorwald]] ([[User talk:Thorwald|talk]]) 03:24, 22 November 2010 (UTC)

== A singularity is not the same as a black hole ==

I made a few edits in the intro when I noticed that TWO distinct definitions were given.  I ultimately saw that these two definitions were intricately muddled throughout the article.

Unless I have some big misunderstandings, a singularity is not the same as a black hole.  

Just because the Schwarzschild radius (an event horizon-like-thing) is at the surface doesn't mean the ability to resist gravitational pressure is all lost and an automatic compression to a singularity ensues.  A "singularity" is defined to have a radius of ZERO, black holes generally don't have a surface radius of zero, they just have a lot of mass and are small enough that the Schwarzschild radius is ''above'' the surface.

In so many places in the article, the SR is referred to as a function of MASS ONLY, which implies it is NOT related to the ability or inability of the matter to resist the gravity pressure, yet in many places the ability to resist gravity pressure and singularities are muddled in with it all.

So, what's the answer?  It's a pretty serious problem and, if you'll forgive me, I'm raising the EXTREMELY DUBIOUS flag for the whole article because of it.

I can't fix it.  I don't have enough detailed background, nor enough time, nor enough inclination for that matter.  But you people who watch this article CAN fix it, and you need to get on it!  It's incredibly bad!

Okay, if I'm out-to-lunch it's no big deal, just explain to me why.  For that matter, explain it in the article itself.  It is unclear in the article just how the ability to resist gravitational pressure is related to the SR being at the surface, etc.  If they are indeed related, please try to make that clear in the article.  I'm a ''really'' smart guy, and it's unclear to me.  :-).

All the best to you all,

Dave (today on IP [[Special:Contributions/108.7.171.191|108.7.171.191]] ([[User talk:108.7.171.191|talk]]) 05:31, 27 May 2011 (UTC))


I looked a little bit up about singularities and is seems that in physics it doesn't necessarily mean surface radius is zero.  Instead, it has a number of different meanings, depending on context, related to the center of a black hole.  Still though, the intermixing of Rsurface = SR with inability to continue to withstand gravity remains dubious or inadequately explained (prior to my quick-fix edits described below).  If "singularity" (and/or the other stuff) is brought back, it should be brought back along with more specific explanation about what "singularity" means in this case.  Also more explanation about why a nonsensical thing like "(Rsurface = SR) = collapse" is true if indeed it is true.  And, since such a thing is an ''extraordinary'' claim, it would need extraordinary and extraordinarily ''reliable'' references! :-)

Dave (today on IP [[Special:Contributions/108.7.171.191|108.7.171.191]] ([[User talk:108.7.171.191|talk]]) 07:24, 27 May 2011 (UTC)

===Taking a shot at fixing it===
On somewhat closer inspection, it looks like the only remaining of these muddlements are a sentence remaining in the intro and a bunch woven into the HISTORY section.  I am going to remove the History section because that is the quickest and easiest way to correct the problem.  I know it's a big hairy deal to delete a section, but if you want to put it back, you are certainly welcome, just please do your best to correct the problem as you do (by removing the muddlements or adding explanation why they aren't muddlements)

Yours,

Dave (today on IP [[Special:Contributions/108.7.171.191|108.7.171.191]] ([[User talk:108.7.171.191|talk]]) 05:49, 27 May 2011 (UTC))

===Wikipedia bugs in evidence here===
I made those changes I described above.  But, they took a long time to show up in the article, AND they haven't yet appeared in the edit history page.  It's been 5 or 6 days so far.  There were other strangenesses while I was doing the edits too (too much to go in to).  So if you want to see the edits, click on "My" IP address above, you'll see they were actually made, they just don't show up in the edit history for some reason.  All other articles I've played with since then are behaving normally.  I am an experienced editor by the way, so I do know when WP is behaving strangely.

Dave (today on another IP: [[Special:Contributions/108.7.162.218|108.7.162.218]] ([[User talk:108.7.162.218|talk]]) 18:11, 2 June 2011 (UTC))

== The Sun has a Schwarzschild radius of app. 3 km (1.86 miles) ==

the [[Sun]] has a Schwarzschild radius of approximately 3.0&nbsp;km (1.86 miles). - Brad Watson, Miami [[Special:Contributions/71.196.121.70|71.196.121.70]] ([[User talk:71.196.121.70|talk]]) 19:44, 11 July 2011 (UTC)

== The top image on the page should be a diagram showing at least one radius ==
The top image on the page should be a diagram showing at least one radius. The Schwarzschild radius might be a good one to include. I don't know what the diagram shown there is but it doesn't seem to have anything to do with gravity or spacetime or light paths.
[[User:McGinnis|Michael McGinnis]] ([[User talk:McGinnis|talk]]) 06:33, 22 July 2011 (UTC)

== The Schwarzschild radius in gravitational time dilation ==

The formula given was 

:<math> \frac{t_r}{t} = \sqrt{1 - \frac{r_s}{r}} = \frac{1}{2}</math>

I removed the 1/2 as it clearly doesn't make sense here, (otherwise tr = 1/2 t regardless of the size of the mass) and doesn't correspond to the formula given in the reference article (http://en.wikipedia.org/wiki/Gravitational_time_dilation) where it says

:<math>t_0 =  t_f \sqrt{1 - \frac{2GM}{rc^2}} = t_f \sqrt{1 - \frac{r_0}{r}} </math>

Neill Jones
[[Special:Contributions/87.113.10.142|87.113.10.142]] ([[User talk:87.113.10.142|talk]]) 15:09, 16 February 2012 (UTC)

== Newtonian derivation ==

A  historical note -- as I recall, it's pointed out in Halliday and Resnick that
the equation r=2Gm/c^2 was first derived in the 1700s sometime.  I suspect it's given as a  problem.  Easy enough to look up, if anyone cares.

: Yep, that would be [[John Michell]]'s 1783 letter to [[Henry Cavendish]], published in the [[Royal Society]]'s journal in  1784. [[User:ErkDemon|ErkDemon]] ([[User talk:ErkDemon|talk]]) 15:11, 28 September 2015 (UTC)

I derived it myself, in high school, by asking what can be said about an object with escape velocity =c - which is in fact the definition of the event horizon of a black hole.

If you want to reproduce it, remember

 f=m a =m d^2x/dt^2 = m dv/dt = m dv/dx dx/dt =   m v dv/dx = GmM/x^2, 

rearrange, and integrate.  I used to give this as an extra credit problem when I was a physics  TA.

Steve Horne (stephen.f.horne@gmail.com)  <span style="font-size: smaller;" class="autosigned">—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/67.90.34.130|67.90.34.130]] ([[User talk:67.90.34.130|talk]]) 16:22, 24 March 2011 (UTC)</span><!-- Template:UnsignedIP --> <!--Autosigned by SineBot-->

: You are assuming Newtonian physics. In which case, <math>v_e = c</math> only gives the boundary from where light cannot escape '''to infinity''' without additional forces. Light can still go outside such a boundary. ... [[Special:Contributions/217.121.224.124|217.121.224.124]] ([[User talk:217.121.224.124|talk]]) 00:08, 1 April 2012 (UTC)
:: That's correct. In a C18th "dark star" model, light from inside r=2M can't escape and reach a distant observer along an unaccelerated ballistic trajectory, but it can "visit" the outside region for a while before being pulled back in. While outside, it can interact with other visiting or passing particles in such a way as to be accelerated free or cause other signals that can escape and be seen by the remote observer, so the "visiting" particles under NM are analogous to [[virtual particle|"virtual" particles"]] under QM, which also cannot be directly detected by the distant observer (in the absence of acceleration), but whose presence has detectable consequences. If the distant observer catches some of this escaping radiation and extrapolates the path backwards, incorrectly assuming a lack of acceleration, they end up with a description in which the particles start outside r=2M as the result of particle-pair-production processes, so the dark star "indirect radiation" effect lets us derive the textbook 1970s description of [[Hawking radiation]]. Also, in a dark star model, an accelerated observer hovering in the region just outside r=2M would be able to see and collect local visiting particles that were defined as "not existing" by the remote observer using GR1916 conventions, so a dark star also supports 1970s [[Unruh radiation]], which, again, GR1916 doesn't. [[User:ErkDemon|ErkDemon]] ([[User talk:ErkDemon|talk]]) 15:11, 28 September 2015 (UTC)
:... Newtonian physics doesn't have event horizons. You '''need''' relativity to derive the Schwarzschild radius in a way that makes sense. [[Special:Contributions/217.121.224.124|217.121.224.124]] ([[User talk:217.121.224.124|talk]]) 00:08, 1 April 2012 (UTC)

:: Kinda. You need GR1916 (or something very similar) in order to derive an ''absolutely black'' non-radiating horizon at r=2M, which corresponds to the GR1916 definitions of how causality is supposed to operate. However, quantum mechanics seems to say that the causal structure of horizons doesn't correspond to the GR1916 version of events, but is closer to the C18th version, with "effective" horizons leaking information and fluctuating and radiating in response to events happening behind them. What "makes sense" according to GR1916 appears according to QM to be badly oversimplified, and somewhat unsophisticated. Simplification allows rigorous mathematical proofs, but ''over''simplification means that these proofs may have nothing to do with the real-world physics. One of the challenges of mathematical physics is knowing when the former starts to become the latter. 
:: The more modern counterpart of a dark star horizon is an [[acoustic metric]] horizon, and [[quantum gravity]] guys sometimes use those to model QM behaviour within a more-easy-to-visualise classical framework, so the Newtonian C18th effects have modern counterparts being explored in the context of cutting-edge C21st research into QG. The big problem that the QG guys have is that nobody can work out how to retrofit these effects to a GR1916-based model. That's why we don't yet have a working theory of quantum gravity that reconciles QM with GR1916. [[User:ErkDemon|ErkDemon]] ([[User talk:ErkDemon|talk]]) 15:11, 28 September 2015 (UTC)

:I really think the entire derivation should just be deleted since it is wrong. This common proof (of setting the Newtonian escape speed to c) is nothing more than a string of naive statements that ultimately just happen to give you the right answer. Specifically, the derivation of the formula <math>R = 2GM/c^2\,</math> is wrong, for at least several reasons: (1) The derivation uses a Newtonian formula for the kinetic energy, (2) the gravitational potential energy is not a well-defined concept, and, most important, (3) a black hole is not simply an object whose escape speed is c at the event horizon. For one, whenever we talk about speeds, we have to be careful about whether they are just coordinate speeds. (It turns out that in the implicit Schwarzschild coordinates, the coordinate speed of all objects at the event horizon is just 0.) Second, the Newtonian concept of escape speed only applies to free particles and simply stating "escape speed is c" does not preclude the possibility of escape via accelerated paths (i.e., rockets).

:I have written much more extensively about this false proof on Reddit's /r/askscience. (See my most recent reference.<ref>https://www.reddit.com/r/askscience/comments/4i8o7x/why_is_the_answer_for_earths_schwarzschild_radius</ref>) I think it's best that the entire derivation just be deleted until someone is ambitious enough to write a new one. An argument using dimensional analysis can be included, but obviously does not consist of a full proof. A full proof would derive the general spherically symmetric vacuum metric and then identify the free parameter as <math>R = 2GM/c^2\,</math> via some appropriate reduction to Newtonian gravity in the weak-field limit. (Also the part at the end of the section about densities and volumes is also not really correct. The volume of a black hole is observer-dependent, and so not well-defined. In Schwarzschild coordinates, the volume is not even defined because the coordinate chart does not cover the interior of the black hole.) [[User:Midtek|Midtek]] ([[User talk:Midtek|talk]]) 19:47, 7 May 2016 (UTC)
{{talkref}}

== "Shield of blackness" ==

"Schwarzschild" translates literally as "black shield" or liberally as "shield of blackness".
To a German newcomer to astrophysics this would be an obvious name for the phenomenon, before being told that this is the name of the discoverer/hypothesizer.  Not unlikely enticed by his own name, the astonomer Karl Schwarzschild thought harder than others of the possibility of a capsule or shield of blackness around a very dense mass.  Half a century had to pass after his death until evidence appeared that this was not just a pipedream.
[[User:Puddington|Puddington]] ([[User talk:Puddington|talk]]) 22:57, 17 June 2012 (UTC)

== Error in the Milky Way's diameter ==

The milky way's diameter as mentioned in the parameter table is incorrect. It is mentioned at ~0.2ly whereas wikipedia on the 'Milky way' page states it as 100-120kly. Please make the necessary change.  <span style="font-size: smaller;" class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/115.242.197.202|115.242.197.202]] ([[User talk:115.242.197.202|talk]]) 16:27, 9 December 2012 (UTC)</span><!-- Template:Unsigned IP --> <!--Autosigned by SineBot-->
:The number quoted in the table is not the Milky Way's diameter, it's its Schwarzschild radius. I didn't check if the number given is correct but it should certainly be much smaller than the diameter. If it was the same we wouldn't be here :-) &mdash;&thinsp;[[User:Hhhippo|<span style="color:darkblue; font-family:times;">'''H<small>HHIPPO</small>'''</span>]] 21:41, 9 December 2012 (UTC)
::I fixed the Milky Way's actual radius which was being quoted as {{val|2.5e20}} but it is more like {{val|5e20}}. However the mass of the Observable Universe is much more problematic [[User:Mmom|Mmom]] ([[User talk:Mmom|talk]]) 14:36, 21 April 2021 (UTC)

== Table of Schwarzchild radii ==
I think the table would be a lot more helpful if instead of showing only the Schwarzschild radius, it also showed the actual radius of the objects. If both of these are next to each other, the reader can better appreciate how far those objects are from black holes. [[User:Reddevyl|Βαll]] ([[User talk:Reddevyl|talk]]) 07:19, 19 December 2012 (UTC)

The Andromeda Galaxy and NGC 4889 are both more massive than the Milky Way, yet the Schwarzschild radius of the Milky Way is the largest in the table. What am I missing?  <!-- Template:Unsigned --><small class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Ianainet|Ianainet]] ([[User talk:Ianainet#top|talk]] • [[Special:Contributions/Ianainet|contribs]]) 06:08, 7 April 2017 (UTC)</small> <!--Autosigned by SineBot-->

== A possible reference for the Schwartzschild Radius of the observable universe ==
There's a nice explanation at: [http://van.physics.illinois.edu/qa/listing.php?id=13892]. I think it should be paraphrased for this article, though I don't have the time to do it myself right now. I may return later, but if someone who is more knowledgeable about relativity could do this, I'd be very appreciative.
[[User:Insurrectionist|Insurrectionist]] ([[User talk:Insurrectionist|talk]]) 05:58, 20 August 2013 (UTC)

''The observable universe's mass has a Schwarzschild radius of approximately 13.7 billion light-years'' - this is very wrong. The source [https://en.wikipedia.org/wiki/Schwarzschild_radius#cite_note-Valev-7] and [https://van.physics.illinois.edu/qa/listing.php?id=13892] assumes the Hubble radius as the radius of the observable universe. The observable universe's (particle horizon) radius [https://en.wikipedia.org/wiki/Cosmological_horizon] is a lot larger (approx. 46.9Gly) than the Hubble radius. The total mass (baryonic 'normal' matter, dark matter and dark energy) of the observable universe (from critical density) is around 3*10^57g so the Schwarzschild radius of the observable Universe is around 475Gly. For an actual credible reference, see: [https://astronomy.stackexchange.com/questions/32443/observable-universe-equals-its-schwarzschild-radius-event-horizon]  --[[User:Electron90|Electron90]] ([[User talk:Electron90|talk]]) 23:10, 4 September 2020 (UTC)

: This is true, however the mass of the Observable Universe quoted here is off by a factor of 10. This is a real problem as there is no general consensus on this mass - but having different values across different pages should be addressed: [[Observable universe]]. The exact value is very important as multiplying the mass by 10 will in fact bring the Schwarzschild to the Hubble radius, thus giving credibility to the [[Black hole cosmology]] theory. If no professional astrophysicists are willing to update this, I eventually will.   [[User:Mmom|Mmom]] ([[User talk:Mmom|talk]]) 14:42, 21 April 2021 (UTC)

:: Where did this value of 8.8E52 kg even come from? [[Observable Universe]] calculates more than this just for the mass of ordinary matter! I'm flagging it. So this value corresponding with the age of the universe is going to have to be corrected as well. I've seen it disputed on [https://physics.stackexchange.com/questions/471160/schwarzschild-radius-of-the-universe Physics Stack Exchange] ([https://9to5science.com/schwarzschild-radius-of-the-universe +]) but more obviously it implies a value for mass of the observable universe that's far too low. [[User:DAVilla|DAVilla]] ([[User talk:DAVilla|talk]]) 15:43, 4 January 2023 (UTC)

== Schwarzschild Radius (1916 version) ==

In the original 1916 paper, alpha='Schwarzschild Radius' arises as a constant of integration and must be computed empirically using the scalar radius r and angular velocity. Nowhere in the 1916 paper does he derive a value alpha=2GM/c^2. Furthermore, his metric differs from that in the modern treatment. His metric does not have a one-way event horizon at alpha where space and time reverse roles as in the modern treatment. See http://de.wikisource.org/wiki/%C3%9Cber_das_Gravitationsfeld_eines_Massenpunktes_nach_der_Einsteinschen_Theorie . And here is an English translation: http://arxiv.org/pdf/physics/9905030v1.pdf <small><span class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Mathdoktor|Mathdoktor]] ([[User talk:Mathdoktor|talk]] • [[Special:Contributions/Mathdoktor|contribs]]) 15:10, 3 September 2013 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot-->

==Incorrect radius for the Universe ==
 
The radius of the observable universe is given in the table as 4.4 x 10^25 m (~4.4 billion light years)
, which is an order of magnitude too small.  I did not correct it (yet) because the number is correctly flagged as needing a reference, which I don't have at the moment.

[[User:Sprite82|Sprite82]] ([[User talk:Sprite82|talk]]) 23:12, 4 September 2014 (UTC)

== Removed incorrect information. ==

|-
| [[Universe]]     ||align="right" | 4.46{{e|25}}{{Citation needed|date=March 2012}} (~4.7 [[light-year|Gly]]) || align="right" | 8{{e|-29}}{{Citation needed|date=March 2012}} (9.9{{e|-30}}<ref>[http://map.gsfc.nasa.gov/universe/uni_matter.html WMAP- Content of the Universe<!-- Bot generated title -->]</ref>)

This information in correct and the paper is flawed.  The paper asserts that because the universe is flat that it is near the critical density, and that's wrong.  The flattness of the universe comes from dark energy, and the mass of the universe is lower than the critical mass.

[[User:Roadrunner|Roadrunner]] ([[User talk:Roadrunner|talk]]) 16:51, 19 December 2014 (UTC)
{{talkref}}

== Excess radius due to curvature of space-time is Rs/6. ==

The excess radius of the curvature of space-time from a massive object is that object's Schwarzchild radius /6.

== Visible universe as black hole ==

In the See Also section, the “classification of black holes by Schwarzschild radius” includes the visible universe “if its density is the critical density.” The idea that the visible universe could be a black hole (regardless of its density) is famously [http://www.preposterousuniverse.com/blog/2010/04/28/the-universe-is-not-a-black-hole/ refuted]; I'm not an expert, but certainly the claim isn't supported by either the [[visible universe]] link or the critical density link, much less a citation.  <small><span class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Luke Maurer|Luke Maurer]] ([[User talk:Luke Maurer|talk]] • [[Special:Contributions/Luke Maurer|contribs]]) 01:25, 10 November 2015 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot-->

: I wouldn't call someone's opinion, in a non-reviewed medium no less, refutation of a very obvious idea, that we, nor light, nor anything else, will ever exit the universe. How exactly that should be phrased, and how strong of a claim can be made to this end, is another matter, but certainly a [[white hole]] as postulated holds some analogy to the inside of a black hole. [[User:DAVilla|DAVilla]] ([[User talk:DAVilla|talk]]) 16:22, 4 January 2023 (UTC)

:: Even if an idea might seem "obvious", it does not belong in WP if we cannot find anything reputable that presents the idea.  No refutation whatsoever is needed.  The mass of the observable universe is not even clearly defined here – for example, it includes the mass density due to the cosmological constant, but this is not mentioned.  The radius of the observable universe is also ill-defined (my guess it is the comoving distance to what emitted observable radiation that we are receiving now, and this has long ago passed the horizon of what we can still receive radiation from that is emitted today.  In all, this is convoluted.  I've just removed it.  —[[User_talk:Quondum|Quondum]] 00:36, 17 April 2023 (UTC)

== This article is garbage. ==

I don't know where to start. The lede, as I read it, says that Rs is a property of a sphere. Wrong. At least on a meta-physics level, Rs is a property of a MASS. And the lede utterly fails to make that clear. It also goes on to talk about compression of a mass, as if that were generally possible. It fails to distinguish spherical mass distributions from alternatives, for instance a long thin wire. It talks about escape velocity (as if that explains anything to someone who doesn't have a good grasp of Freshman physics). It talks about light not able to "escape" from an star's surface, yet BHs emit light (called Hawking Radiation (although I realize that it is moot whether HR is "escaping", what is meant by surface, etc.)) It talks about a "sphere". Does it mean a ball (3 dimensional) or a surface (2 dimensional)? In other words, the lede makes all sorts of unwarranted assumptions about the reader's interpretation of its quite poor choice of words. Rs is a property of any mass which is defined to be the distance from a point of that given mass at which the escape velocity is the speed of light. Earth's Rs is a bit more than one-third of an inch (0.89 cm) (see table). I visited this article previously and it was much better then. The Formula section is virtually incomprehensible and is an extremely LOUSY attempt to DERIVE the formula. Here are my suggestions. Define the terms of the equation. For instance, no where do I see a clear explanation that M is rest mass...or is it? Rs clearly depends NOT just on mass of an object, but on its total energy. You'd think that would be made clear. Anyway, why not clean up all the garbage? 
<br />
Formula<br />
Rs is directly proportional to Mass(energy). Rs ∝ M.<br />
The proportionality constant is 2G/c² where G is the UNIVERSAL Gravitational Constant and c is the absolute Speed of Light.<br />
Rs = 2GM/c²<br />

all the rest is superfluous.(and the lame attempt at a derivation is risible...limiting maximum radius of a massive object indeed.)[[Special:Contributions/216.96.79.179|216.96.79.179]] ([[User talk:216.96.79.179|talk]]) 16:01, 29 January 2016 (UTC)

== Wrong formula for potential energy ==

In the section [[Schwarzschild_radius#Formula|Formula]], the formula for potential energy, GMm/r, cannot be used. This formula assumes that the masses are constant. Obviously, relativistic mass is not. At best, it's an upper bound on the energy but would be too high to calculate the event horizon. [[User:Shawncorey|Shawn H Corey]] ([[User talk:Shawncorey|talk]]) 14:05, 15 June 2016 (UTC)
==Needs attention from an expert, or deletion==
This article appears to have been written by people who don't know any general relativity. The section titled "Formula" is at best a pseudo-derivation using Newtonian gravity, but it isn't labeled as such. I'm going to add a tag to say that it needs attention from an expert. It might actually make more sense to delete it, since the relevant information is contained in the article [[Black hole]].--[[Special:Contributions/76.169.116.244|76.169.116.244]] ([[User talk:76.169.116.244|talk]]) 22:37, 10 August 2016 (UTC)
:{{Done}} Replaced with link to existing Derivation article. <small>[[User talk:NE Ent|NE Ent]]</small> 17:34, 7 October 2016 (UTC)

== fictional theory ==
a black hole doesn't choose to rotate, it fundamentally rotates, nothing has to initiate that rotation, that's the only way space-time works at these degenerate concentrations of energy. Some people claim allow some myth in order we test rare cases, but the point is that fake physics doesn't leed to solutions but mistakes.  <!-- Template:Unsigned IP --><small class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/2A02:587:4110:2B00:F0D5:204:77E2:3637|2A02:587:4110:2B00:F0D5:204:77E2:3637]] ([[User talk:2A02:587:4110:2B00:F0D5:204:77E2:3637#top|talk]]) 19:08, 23 October 2016 (UTC)</small> <!--Autosigned by SineBot-->

== The Schwarzschild radius and the Einstein equations ==

In this article, we should pay attention to the fact that the expression for the [[Schwarzschild radius]] <math>r_s =2\,G\,M/c^2=2\,(G/c^3)\,Mc</math> in form coincides with the integral form of the [[Einstein equations]] for a small region of spacetime: <math>R_i=2\,(G/c^3)P_i=2\,(G/c^3)\,Mc\,U_i=r_s\,U_i</math>, where <math>R_i</math> is the <math>i</math>-component of the Schwarzschild radius <math>r_s</math>; <math>P_i</math> is the [[four-momentum]] of matter; <math>U_i</math> is the [[four-velocity]]. See details [https://en.wikipedia.org/w/index.php?title=Planck_length&diff=621741916&oldid=621542882  '''here'''] in the second proof. [[Special:Contributions/178.120.43.16|178.120.43.16]] ([[User talk:178.120.43.16|talk]]) 08:20, 3 April 2017 (UTC)

== Error in sizes table ==
I've just been writing a R(s) to-from Mass tool for my "toolbox spreadsheet", and checking it against the data here.
The Earth, for example, for a mass of 5.98E+24kg gives a R(s) of 0.00887m, which is right (9mm) ; Sun, 2E+30kg, 2968m (3km) ; 70kg human, 1.03895420951896E-25m ... which is twice the size given.
I've corrected the table by doubling the "human" data line for a 35 kg child and a 70kg adult. The simple factor-of-2 difference may make the point of the simple proportionality between mass and R(s).

I don't have independent mass data for SgrA*, or the Andromeda SMBH.
[[User:A Karley|AKarley]] ([[User talk:A Karley|talk]]) 11:07, 5 September 2017 (UTC)
:It's very interesting that the larger the mass of a black hole (or its progenitor object), the lower the density inside the hole. Most people naturally assume that if matter is compressed to the point where not even light can escape it, then it will end up at roughly the same density no matter how much matter there was in the progenitor. But instead, if a notional solar-mass black hole had the same high density as its notional earth-mass counterpart, the radius of the former would be in the range of 70 cm, not 3 km! [[Special:Contributions/188.150.64.57|188.150.64.57]] ([[User talk:188.150.64.57|talk]]) 05:21, 25 February 2023 (UTC)

== Wrong notation? Shouldn't it be 'R sub g' instead of 'r sub s'? ==

According to the [https://www.britannica.com/science/Schwarzschild-radius Encyclopædia Britannica], the notation specifically for the Schwarzschild radius of an object is "Rg" (R sub g), not (r sub s).

Or am I stale in my understanding? Be kind.. [[User:Coar|Rodent of Unusual Size]] ([[User talk:Coar|talk]]) 07:13, 1 July 2019 (UTC)

== Sch. R. is the Abbreviation for Schwarzschild Radius ==

Schwarzschild radius has an abbreviation: '''Sch. R.''' [[Special:Contributions/2601:580:7:7AE8:457C:E737:3CD4:D165|2601:580:7:7AE8:457C:E737:3CD4:D165]] ([[User talk:2601:580:7:7AE8:457C:E737:3CD4:D165|talk]]) 16:01, 18 April 2020 (UTC)

== Planck/natural units ==

To explain [https://en.wikipedia.org/w/index.php?title=Schwarzschild_radius&type=revision&diff=1045290592&oldid=1045288935 this edit] and [https://en.wikipedia.org/w/index.php?title=Schwarzschild_radius&diff=next&oldid=1045290691 this revert], ''nobody writes the Schwarzschild radius as a multiple of the Planck length.'' It's a completely unilluminating exercise in elementary algebra, and it gets the purpose of natural unit systems entirely backwards. The point of [[Planck units]], or any other system of [[natural units]], is to show the essence of the equations by eliminating features that depend upon arbitrary historical conventions. So, if you invoke Planck units at all, you're going to set <math>G = c = 1</math> and just say <math>r_s = 2M</math>. [[User:XOR&#39;easter|XOR&#39;easter]] ([[User talk:XOR&#39;easter|talk]]) 20:47, 19 September 2021 (UTC)

: There's no merit in your  arguments ''nobody does something...'', ''It's a completely unilluminating...''. Quoting ''the Master'': "Everyone knew it was impossible, until a fool who didn't know came along and did it". 

:It's about the beauty of mathematics not about illumination. What illuminates you may not be illuminating to me but <math>r_s = \frac{2 G M }{c^2}</math> remains <math> r_s = 2m l_\text{P} </math>, where <math>M \equiv {m}{m_\text{P}}</math>, <math>m \in \mathbb{R}</math>, <math>m_\text{P}</math> is [[Planck mass]], and <math>l_\text{P}</math>is [[Planck length]].

:I do wish we could have asked [[Max Planck]] who introduced [[Planck units]] in 1899 about a ''forward'' direction of his unit system. That indeed would have been illuminating to me.  Quoting ''the Master'' again "Imagination is more important than knowledge". I imagine where I'm heading but a lot of research remains to eventually and convincingly prove this direction. However, such little hints like this one show me that this direction is right. [[User:Guswen|Guswen]] ([[User talk:Guswen|talk]]) 05:24, 20 September 2021 (UTC)

::[[User:XOR&#39;easter|XOR&#39;easter]] is trying to teach you something. I advise listening. The more fundamental problem with "nobody does something" is that if you're the only one doing it, it is considered [[WP:OR|original research]], which is not allowed in Wikipedia. [[User:Tercer|Tercer]] ([[User talk:Tercer|talk]]) 07:56, 20 September 2021 (UTC)

::: I wouldn't have called it "a research". As [[User:XOR&#39;easter|XOR&#39;easter]] correctly teaches me, it is rather an "exercise in elementary algebra". We seem to  disagree with [[User:XOR&#39;easter|XOR&#39;easter]] only on the point of "illumination". [[User:Guswen|Guswen]] ([[User talk:Guswen|talk]]) 08:05, 20 September 2021 (UTC)

::: A similar "exercise in elementary algebra" shows that [[Hawking radiation]] from a [[Schwarzschild metric|Schwarzschild]] black hole in [[SI units]] 
:::<math>T = \frac{\hbar\,c^3}{8\pi G k_\text{B} M} </math>,
:::where {{mvar|ħ}} is the [[reduced Planck constant]], {{mvar|c}} is the [[speed of light]], {{math|''k''<sub>B</sub>}} is the [[Boltzmann constant]], {{mvar|G}} is the [[gravitational constant]], and {{mvar|M}} is the [[mass]] of the black hole can be simplified to
:::<math>T = \frac{T_\text{P}}{{2{\pi}d}}</math>
:::where black hole diameter <math>D \equiv d l_\text{P}</math>, <math>d \in \mathbb{R}</math> and <math>T_\text{P}</math> denotes [[Planck units|Planck temperature]]. [[User:Guswen|Guswen]] ([[User talk:Guswen|talk]]) 08:12, 20 September 2021 (UTC)

::::Indeed, your original research consists of exercises in elementary algebra. The point is that nobody writes the units <math>T_\text{P}</math> and <math>l_\text{P}</math> explicitly like this. You are complicating, when the purpose was to simplify. I see you also added your pointless complication to [[Hawking radiation]], I'll remove it from there as well. [[User:Tercer|Tercer]] ([[User talk:Tercer|talk]]) 08:28, 20 September 2021 (UTC)

:::::Why do you call a simplification "complicating"? Original Hawking radiation formula depends on 4 physical constants. This simplification depends on only one (<math>T_\text{P}</math>). [[User:Guswen|Guswen]] ([[User talk:Guswen|talk]]) 08:32, 20 September 2021 (UTC)

::::::Because the formula for Hawking radiation temperature in Planck units is <math>\frac1{8\pi M}</math>. Yours is more complicated than that. [[User:Tercer|Tercer]] ([[User talk:Tercer|talk]]) 08:51, 20 September 2021 (UTC)

::::::: True. But we are considering [[SI units]] not [[Planck units]] versions of a black hole radius and temperature  formulas here. [[User:Guswen|Guswen]] ([[User talk:Guswen|talk]]) 09:02, 20 September 2021 (UTC)

::::::::Your formula uses the "Schwarzschild diameter" in Planck units. In SI units your formula would be <math>\frac{T_p l_p}{2\pi D}</math>. [[User:Tercer|Tercer]] ([[User talk:Tercer|talk]]) 09:27, 20 September 2021 (UTC)

:::::::: I disagree. <math>T = \frac{T_\text{P}}{{2{\pi}d}}</math> is not in [[Planck units]] but in [[SI units]], where temperature is measured in [[Kelvin]]s and mass in [[kilogram]]s.
:::::::: Indeed <math>T = \frac1{8\pi M}</math> is in [[Planck units]]. [[User:Guswen|Guswen]] ([[User talk:Guswen|talk]]) 09:55, 20 September 2021 (UTC)

:::::::::This is not a matter of opinion. ''d'' is measured in Planck lengths. [[User:Tercer|Tercer]] ([[User talk:Tercer|talk]]) 11:44, 20 September 2021 (UTC)
:::Read the [[WP:NOR|No original research]] policy. Then read it again. All your additions are like if someone came along and said, "We learned in school that <math>F = ma</math>. But I propose that the real equation is <math>a = F/m</math> instead." There's no insight; it's just shuffling symbols around. If something ''could'' be discovered by elementary algebra, it would have been already, because physicists all know elementary algebra. Even if, by some extraordinarily improbable series of events, thousands of scientists missed something that took only elementary algebra to see, Wikipedia would not be the right place to advertise it. We follow the scientific community; we don't attempt to lead it. [[User:XOR&#39;easter|XOR&#39;easter]] ([[User talk:XOR&#39;easter|talk]]) 16:30, 20 September 2021 (UTC)
::::I am not advertising anything. I just show some elementary algebra for any one who wants to see it. But I also know that you got this feeling that soon you'll have to revert all your edits. For now keep the system closed. Let them sleep like babies tonight. [[User:Guswen|Guswen]] ([[User talk:Guswen|talk]]) 23:10, 21 September 2021 (UTC)

== Image ==

[[File:Triangle of everything simplified 2 triangle of everything - Planck Units.png | thumb|upright=1.5 | In a mass-radius plot, the Schwarzschild radius represents the upper limit of any object that can exist (the [[Compton Wavelength]] and [[Hubble radius]] being other 2 limits forming a triangle). It's intersection with the Compton Wavelength defines all [[Planck Units]]. ]]

Since the article was missing an image, I added this one, where it shows the importance of the schwarzchild radius not only for black holes but for cosmology as a whole. I hope you like it and I'm open to criticism on how it can be improved. [[User:Avsa|Alex Van de Sande]] ([[User talk:Avsa|talk]]) 17:38, 20 February 2025 (UTC)

== Confusion of two concepts ==

The statement that the '''Schwarzschild radius''' is the '''gravitational radius''' creates confusion.<br>
The quantity <math> r_g = Gm/c^2 </math> (the ''gravitational radius'' of the mass <math> m </math>) was introduced by the German theorist [[Hermann Weyl]] in his ''Gravity and Electricity'' (1918). <br>
This value follows directly from the formula for the [[coupling constant]] of gravitational interaction: <math>\alpha_g = Gm^2/\hbar c </math>.

Using the equality '''''ћ'' = ƛ''mc''''' we get: '''''Gm''<sup>2</sup> = α<sub>''g''</sub>''ћc'' = α<sub>''g''</sub>ƛ''mc''<sup>2</sup> = ''r''<sub>''g''</sub>''mc''<sup>2</sup>''', where '''''r''<sub>''g''</sub> = α<sub>''g''</sub>ƛ = ''mG''/''c''<sup>2</sup>'''. <br>

There is no need to mention the expression "gravitational radius" in the article. This will allow us to separate these two different concepts and create a new article "'''Gravitational radius'''" in Weyl's understanding. <br>
-- [[User:Aab64|Aab64]] ([[User talk:Aab64|talk]]) 05:12, 9 May 2025 (UTC)

:The gravitational radius content here was based on two fringe sources by the same author. I deleted both and the claim related to the equivalence to the Schwarzschild parameter. [[User:Johnjbarton|Johnjbarton]] ([[User talk:Johnjbarton|talk]]) 17:30, 9 May 2025 (UTC)