Living Reviews in Relativity

"The Kerr/CFT Correspondence and its Extensions"
Geoffrey Compère 

Hide Subsections

1 Introduction
1.1 Classes of effective field theories
1.2 Gauge fields as Kaluza–Klein vectors
2 Extremal Black Holes as Isolated Systems
2.1 Properties of extremal black holes
2.2 Near-horizon geometries of static extremal black holes
2.3 Near-horizon of extremal spinning geometries
2.4 Explicit near-horizon geometries
2.5 Entropy
2.6 Temperature and chemical potentials
2.7 Near-extremal near-horizon geometries
2.8 Uniqueness of stationary near-horizon geometries
2.9 Absence of bulk dynamics in near-horizon geometries
3 Two-Dimensional Conformal Field Theories
3.1 Cardy’s formula
3.2 DLCQ and chiral limit of CFTs
3.3 Long strings and symmetric orbifolds
4 Microscopic Entropy of Extremal Black Holes
4.1 Boundary conditions and asymptotic symmetry algebra
4.2 Absence of SL (2,ℝ ) asymptotic symmetries
4.3 Virasoro algebra and central charge
4.4 Microscopic counting of the entropy
5 Scattering from Near-Extremal Black Holes
5.1 Near-extremal Kerr–Newman black holes
5.2 Macroscopic greybody factors
5.3 Macroscopic greybody factors close to extremality
5.4 Microscopic greybody factors
5.5 Microscopic accounting of superradiance
6 Hidden Symmetries of Non-Extremal Black Holes
6.1 Scalar wave equation in Kerr–Newman
6.2 Scalar wave equation in Kerr–Newman–AdS
6.3 Near-region scalar-wave equation
6.4 Local SL (2, ℝ) × SL (2,ℝ ) symmetries
6.5 Symmetry breaking to U (1 )L × U (1)R
6.6 Entropy matching
7 Summary and Open Problems
7.1 Summary
7.2 Set of open problems
8 Acknowledgments
Open References References