Electrovacuum Near-horizon Geometries in Four and Five Dimensions

TL;DR

This paper reviews and advances the classification of near-horizon geometries of extremal black holes in four and five dimensions, focusing on Einstein-Maxwell solutions with a negative cosmological constant and supersymmetric cases in supergravity.

Contribution

It provides a classification of near-horizon geometries for extremal black holes in four-dimensional Einstein-Maxwell theory and five-dimensional supergravity, including non-supersymmetric cases.

Findings

Classification of near-horizon geometries in 4D Einstein-Maxwell with negative cosmological constant.

Progress in classifying supersymmetric near-horizon geometries in 5D supergravity.

Discussion of recent advances in non-supersymmetric extremal black hole geometries.

Abstract

Associated to every stationary extremal black hole is a unique near-horizon geometry, itself a solution of the field equations. These latter spacetimes are more tractable to analyze and most importantly, retain properties of the original black hole which are intrinsic to the event horizon. After reviewing general features of near-horizon geometries, such as SO(2,1) symmetry enhancement, I report on recent work on stationary, charged extremal black hole solutions of the Einstein-Maxwell equations with a negative cosmological constant in four dimensions and present a classification of near-horizon geometries of black holes on this kind. In five dimensions, charged extremal black hole solutions to minimal (gauged) supergravity, which arises naturally in string theory and the gauge theory/gravity correspondence, are considered. I consider the classification of near-horizon geometries for the subset of such black holes which are supersymmetric. Recent progress on the classification problem in the general extremal, non-supersymmetric case is also discussed.