Classification of near-horizon geometries of extremal black holes

TL;DR

This paper reviews the classification of near-horizon geometries of extremal black holes across various theories and dimensions, highlighting symmetry properties, topologies, and recent advances in understanding their structure.

Contribution

It provides a unified review of near-horizon geometries, discusses classification results, and presents new findings and open problems in the field.

Findings

Horizon topology constraints for extremal black holes

Symmetry enhancement in near-horizon geometries

Progress in classifying geometries in diverse theories

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.