Black Hole Entropy from Conformal Field Theory in Any Dimension

TL;DR

This paper argues that black hole entropy has a universal statistical-mechanical origin tied to horizon-local conformal symmetry. By analyzing the surface deformation algebra near the horizon, it identifies a Virasoro subalgebra with a calculable central charge and applies Cardy's formula to count horizon microstates. The resulting entropy matches the Bekenstein-Hawking expression $S_{BH}=A/4G$ and is presented as independent of the details of the underlying quantum gravity theory. The work also discusses open questions about the precise nature of the microstates and potential links to Liouville-type reductions or boundary-induced gauge degrees of freedom.

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.