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"Classification of Near-Horizon Geometries of Extremal Black Holes"
Hari K. Kunduri and James Lucietti
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Abstract
1
Introduction
1.1
Black holes in string theory
1.2
Gauge/gravity duality
1.3
Black hole classification
1.4
This review
2
Degenerate Horizons and Near-Horizon Geometry
2.1
Coordinate systems and near-horizon limit
2.2
Curvature of near-horizon geometry
2.3
Einstein equations and energy conditions
2.4
Physical charges
3
General Results
3.1
Horizon topology theorem
3.2
AdS
2
-structure theorems
4
Vacuum Solutions
4.1
Static: all dimensions
4.2
Three dimensions
4.3
Four dimensions
4.4
Five dimensions
4.5
Higher dimensions
5
Supersymmetric Solutions
5.1
Four dimensions
5.2
Five dimensions
5.3
Six dimensions
5.4
Ten dimensions
5.5
Eleven dimensions
6
Solutions with Gauge Fields
6.1
Three dimensional Einstein–Maxwell–Chern–Simons theory
6.2
Four dimensional Einstein–Maxwell theory
6.3
Five dimensional Einstein–Maxwell–Chern–Simons theory
6.4
Theories with hidden symmetry
6.5
Non-Abelian gauge fields
7
Applications and Related Topics
7.1
Black-hole uniqueness theorems
7.2
Stability of near-horizon geometries and extremal black holes
7.3
Geometric inequalities
7.4
Analytic continuation
7.5
Extremal branes
Acknowledgements
References
Footnotes
The emergence of an AdS
3
factor for solutions with certain null singularities has been previously observed
[
68
,
18
]
. We
will only consider regular horizons, so the area of spatial cross sections of the horizon is necessarily non-zero.