Living Reviews in Relativity

"Classification of Near-Horizon Geometries of Extremal Black Holes"
by
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 AdS2-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