Near-horizon geometry and black holes in four dimensions

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. (C) 1998 Elsevier Science B.V.