The Kerr/CFT Correspondence and its Extensions

• Published in: Living reviews in relativity Vol. 15; no. 1; p. 11
• Main Author: Compère, Geoffrey
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.01.2012; Springer Nature B.V; SpringerOpen
• Subjects: AdS/CFT; Astrophysics and Astroparticles; Asymptotic properties; Black holes; Classical and Quantum Gravitation; conformal field theory; Cosmology; First principles; holography; Physics; Physics and Astronomy; Quantum field theory; Quantum theory; Relativity Theory; Review; Review Article; Extremal Black Hole; Black Hole; Hide Conformal Symmetry; Asymptotic Symmetry Algebra; Kerr Black Hole
• ISSN: 2367-3613; 1433-8351; 1433-8351
• DOI: 10.12942/lrr-2012-11

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 SL (2, ℤ) 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.