Near Horizon Geometry and Black Holes in Four Dimensions

TL;DR

This paper explores the near horizon geometries of four-dimensional black holes in M-theory, showing how their microstates can be counted using conformal symmetry on AdS boundaries, aligning with the Bekenstein-Hawking law.

Contribution

It demonstrates that extremal black holes' near horizon geometries relate to AdS_3 spaces and extends the conformal field theory approach to orbifolds of AdS spaces.

Findings

Microstates count matches Bekenstein-Hawking entropy

Near horizon geometries derived from AdS_3 by identifications

Extension of boundary CFT analysis to AdS orbifolds

Abstract

A large class of extremal and near-extremal four dimensional black holes in M-theory feature near horizon geometries that contain three dimensional asymptotically anti-de Sitter spaces. Globally, these geometries are derived from AdS_3 by discrete identifications. The microstates of such black holes can be counted by exploiting the conformal symmetry induced on the anti-de Sitter boundary, and the result agrees with the Bekenstein-Hawking area law. This approach, pioneered by Strominger, clarifies the physical nature of the black hole microstates. It also suggests that recent analyses of the relationship between boundary conformal field theory and supergravity can be extended to orbifolds of AdS spaces.