Classification of near-horizon geometries of extremal black holes

Abstract

Any spacetime containing a degenerate Killing horizon, such as an extremal black hole, possesses a well-defined notion of a near-horizon geometry. We review such near-horizon geometry solutions in a variety of dimensions and theories in a unified manner. We discuss various general results including horizon topology and near-horizon symmetry enhancement. We also discuss the status of the classification of near-horizon geometries in theories ranging from vacuum gravity to Einstein-Maxwell theory and supergravity theories. Finally, we discuss applications to the classification of extremal black holes and various related topics. Several new results are presented and open problems are highlighted throughout.

70 pages; invited review article for Living Reviews in Relativity; v2 some improvements and references added

References in corpus (47)

• Building an AdS/CFT superconductor
• Near-horizon symmetries of extremal black holes
• A Higher Dimensional Stationary Rotating Black Hole Must be Axisymmetric
• Quantum Entropy Function from AdS(2)/CFT(1) Correspondence
• Supersymmetric multi-charge AdS_5 black holes
• Kerr-AdS/CFT Correspondence in Diverse Dimensions
• Uniqueness theorem for 5-dimensional black holes with two axial Killing fields
• Gravitational Perturbations of Higher Dimensional Rotating Black Holes: Tensor Perturbations
• An instability of higher-dimensional rotating black holes
• No Dynamics in the Extremal Kerr Throat
• Black Hole Microstates and Attractor Without Supersymmetry
• A classification of near-horizon geometries of extremal vacuum black holes
• Symmetries of Higher Dimensional Black Holes
• Kerr-CFT and gravitational perturbations
• Classical instability of Kerr-AdS black holes and the issue of final state
• Microstates of a Neutral Black Hole in M Theory
• Cargese Lectures on the Kerr/CFT Correspondence
• Gravitational instability of an extreme Kerr black hole
• Algebraic classification of higher dimensional spacetimes based on null alignment
• Extremal vacuum black holes in higher dimensions
• A scalar field condensation instability of rotating anti-de Sitter black holes
• Three-dimensional Chern-Simons black holes
• Perturbations of near-horizon geometries and instabilities of Myers-Perry black holes
• Near-horizon geometries of supersymmetric AdS(5) black holes
• Uniqueness of near-horizon geometries of rotating extremal AdS(4) black holes
• Extremal Isolated Horizon/CFT Correspondence
• 1/16-BPS Black Holes and Giant Gravitons in the AdS_5 X S^5 Space
• On the `Stationary Implies Axisymmetric' Theorem for Extremal Black Holes in Higher Dimensions
• Nonlinear instability of scalar fields on extremal black holes
• Moduli and (un)attractor black hole thermodynamics
• Counting the Microstates of a Kerr Black Hole
• Extremal Black Holes and First Law of Thermodynamics
• On the smoothness of static multi-black hole solutions of higher-dimensional Einstein-Maxwell theory
• A General Black String and its Microscopics
• Heterotic horizons, Monge-Ampere equation and del Pezzo surfaces
• Comments on Charges and Near-Horizon Data of Black Rings
• An infinite class of extremal horizons in higher dimensions
• Index theory and dynamical symmetry enhancement near IIB horizons
• Supersymmetric isolated horizons in ADS spacetime
• Counting the microstates of a vacuum black ring
• A note on degeneracy, marginal stability and extremality of black hole horizons
• Two remarks on near-horizon geometries
• Extremal Sasakian horizons
• Constructing near-horizon geometries in supergravities with hidden symmetry
• Topology of supersymmetric N=1, D=4 supergravity horizons
• Uniqueness of extreme horizons in Einstein-Yang-Mills theory
• Instability in near-horizon geometries of even-dimensional Myers-Perry black holes

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