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{{short description|Black hole solution of general relativity}}
{{More citations needed|date=December 2024}}

In [[theoretical physics]], an '''anti-de Sitter''' ('''AdS''') '''black hole''' is a [[black hole]] solution of [[general relativity]] or its extensions which represents an isolated massive object, but with a negative [[cosmological constant]].  Such a solution [[asymptotically]] approaches [[anti-de Sitter space]] at spatial infinity, and is a generalization of the [[Kerr metric|Kerr vacuum solution]], which asymptotically approaches [[Minkowski spacetime]] at spatial infinity.<ref>{{Citation |last=Fan |first=Zhong-Ying |title=Critical phenomena of regular black holes in anti-de Sitter space-time |journal=The European Physical Journal C |date=2016-09-21 |volume=77 |issue=4 |doi=10.1140/epjc/s10052-017-4830-9 |arxiv=1609.04489}}</ref>

In 3+1 dimensions, the metric is given by
<math display=block>ds^2 = - \left( k^2r^2 + 1 - \frac{C}{r} \right)dt^2 + \frac{1}{k^2r^2 + 1 - \frac{C}{r}}dr^2 + r^2 d\Omega^2</math>
where {{mvar|t}} is the time coordinate, {{mvar|r}} is the radial coordinate, {{math|Ω}} are the [[polar coordinate]]s, {{mvar|C}} is a constant and {{mvar|k}} is the AdS curvature.

In general, in {{math|''d'' + 1}} dimensions, the metric is given by
<math display=block>ds^2 = - \left( k^2r^2 + 1 - \frac{C}{r^{d-2}} \right)dt^2 + \frac{1}{k^2r^2 + 1 - \frac{C}{r^{d-2}}}dr^2 + r^2 d\Omega^2</math>

According to the [[AdS/CFT correspondence]], if gravity were quantized, an AdS black hole would be dual to a thermal state on the conformal boundary. In the context of say, [[AdS/QCD]], this would correspond to the [[deconfinement]] phase of the [[quark–gluon plasma]].

==See also==
* [[BTZ black hole]]
* [[Black brane]]

==References==
{{reflist}}

{{DEFAULTSORT:Ads Black Hole}}
[[Category:Black holes]]
[[Category:Exact solutions in general relativity]]


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