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.
Highlights
Living Reviews in Relativity is a peer reviewed open access journal published by the Max Planck Institute for Gravitational Physics, Am Muhlenberg 1, 14476 Potsdam, Germany
We describe a number of general results concerning the topology and symmetry of near-horizon geometries under various assumptions
Homogeneous, non-static near-horizon geometry is locally isometric to the near-horizon limit of the extremal Myers–Perry black hole with SU (2) × U (1) rotational symmetry
Summary
Equilibrium black-hole solutions to Einstein’s equations have been known since the advent of general relativity. Proportional to the surface gravity κ of the horizon, and possesses a large entropy Deriving these semi-classical thermodynamic formulae from statistical mechanics requires a microscopic understanding of the “degrees of freedom” of the black hole. This has been a major motivation and driving force for quantum gravity research over the last four decades, it is fair to say this is still poorly understood.
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