Black Hole Entropy from Conformal Field Theory in Any Dimension

Abstract

Restricted to a black hole horizon, the “gauge” algebra of surface deformations in general relativity contains a Virasoro subalgebra with a calculable central charge. The fields in any quantum theory of gravity must transform accordingly, i.e., they must admit a conformal field theory description. Applying Cardy's formula for the asymptotic density of states, I use this result to derive the Bekenstein-Hawking entropy. This method is universal—it holds for any black hole, and requires no details of quantum gravity—but it is also explicitly statistical mechanical, based on counting microscopic states.