Classification of Near-Horizon Geometries of Extremal Black Holes

Hari K. Kunduri 
Department of Mathematics and Statistics,
Memorial University of Newfoundland,
St John’s NL A1C 4P5, Canada

James Lucietti 
School of Mathematics and Maxwell Institute of Mathematical Sciences
University of Edinburgh,
King’s Buildings, Edinburgh, EH9 3JZ, UK


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.

Keywords: Black holes, Extremal black holes, Near-horizon geometry

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