We present a first-principles derivation of the main results of the Kerr/CFT correspondence
and its extensions using only tools from gravity and quantum field theory, filling a few
gaps in the literature when necessary. Firstly, we review properties of extremal black holes
that imply, according to semi-classical quantization rules, that their near-horizon quantum
states form a centrally-extended representation of the one-dimensional conformal group.
This motivates the conjecture that the extremal Kerr and Reissner–Nordström black holes
are dual to the chiral limit of a two-dimensional CFT. We also motivate the existence
of an family of two-dimensional CFTs, which describe in their chiral limit the
extremal Kerr–Newman black hole. We present generalizations in anti-de Sitter spacetime
and discuss other matter-coupling and higher-derivative corrections. Secondly, we show how a
near-chiral limit of these CFTs reproduces the dynamics of near-superradiant probes around
near-extremal black holes in the semi-classical limit. Thirdly, we review how the hidden
conformal symmetries of asymptotically-flat black holes away from extremality, combined with
their properties at extremality, allow for a microscopic accounting of the entropy of non-extremal
asymptotically-flat rotating or charged black holes. We conclude with a list of open problems.
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http://www.livingreviews.org/lrr-2012-11 |
Living Rev. Relativity 15, (2012), 11
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