Black Hole Entropy from Conformal Field Theory in Any Dimension

TL;DR

This paper derives black hole entropy universally using conformal field theory techniques, specifically Cardy's formula, linking surface deformations in general relativity to microscopic state counting without relying on quantum gravity details.

Contribution

It introduces a universal method to compute black hole entropy via conformal field theory, applicable to any black hole without specific quantum gravity assumptions.

Findings

Derives Bekenstein-Hawking entropy from CFT methods

Establishes a Virasoro algebra at the black hole horizon

Provides a statistical mechanical interpretation of black hole entropy

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.