"The Kerr/CFT Correspondence and its Extensions"
by
Geoffrey Compère
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Abstract
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
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
symmetries
6.5
Symmetry breaking to
6.6
Entropy matching
7
Summary and Open Problems
7.1
Summary
7.2
Set of open problems
8
Acknowledgments
References
Footnotes