Near Horizon Geometry and Black Holes in Four Dimensions

TL;DR

The work investigates the microscopic origin of entropy for extremal and near-extremal four-dimensional black holes in M-theory by isolating the near-horizon region, which contains an AdS3 factor. This leads to a 3D BTZ-like description with a boundary CFT whose central charge, computable via Brown-Henneaux, reproduces the Bekenstein-Hawking entropy through Cardy counting, including a left-right split. By connecting to M-theory via intersecting M5-branes and a decoupling limit, the authors derive an effective 3D gravity theory with c = 6 n1 n2 n3 and show the entropy matches macroscopic predictions, thereby supporting a holographic, orbifold-extended AdS3/CFT interpretation. The results illuminate the nature of black-hole microstates and suggest a broader applicability of AdS/CFT to orbifolds, while leaving open questions about describing the interior behind the horizon in a unitary CFT framework.

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.