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AdS/CFT is famous correspondence between gravity and CFT.

What one can say about black holes using this correspondence?

What CFT object correspondent for black hole? For charged black hole? Rotating black hole?

What kind of information about black hole one can extract from this correspondence?

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When a Black Hole is present in a bulk, it gives the background some temperature due to Hawking radiation. Thus a stable spacetime in presence of a generic BH has a fixed tempertature $T$. The dual CFT theory also has thermal states. It has been recently shown that these thermal states have one-to-one correspondence with the Black Hole backgrounds of AdS spacetime. Although for extremal black holes(BH with $T=0$) one must take an appropriate limit. Charged, rotating black holes usually have non-zero temperature and hence the above prescription follows.

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  • $\begingroup$ What is differences between different black holes? $\endgroup$ – Nikita Mar 27 '20 at 14:15
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    $\begingroup$ To this answer I would add that charged and spinning black holes have the effect of introducing a chemical potential for the associated symmetry in the boundary theory. $\endgroup$ – MannyC Mar 27 '20 at 14:16
  • $\begingroup$ I think @MannyC 's comment answers Nikita's. $\endgroup$ – Ari Mar 27 '20 at 14:19
  • $\begingroup$ @MannyC what kind of information about black hole one can extract from this correspondence? $\endgroup$ – Nikita Mar 27 '20 at 19:51

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