1203.3561 (Geoffrey Compère)

The Kerr/CFT correspondence and its extensions: a comprehensive review    [PDF]

Geoffrey Compère

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-Nordstr\"om black holes are dual to the chiral limit of a two-dimensional conformal field theory. We also motivate the existence of a SL(2,Z) family of two-dimensional conformal field theories 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.

View original: http://arxiv.org/abs/1203.3561