Black hole entropy from classical Liouville theory

TL;DR

This paper derives black hole entropy by identifying a classical Virasoro algebra in a Liouville theory obtained through dimensional reduction, linking conformal symmetry to black hole microstates.

Contribution

It introduces a novel approach to compute black hole entropy using classical Liouville theory and Virasoro algebra without quantum effects.

Findings

Derives a classical central charge for the Virasoro algebra

Shows the conformal factor obeys a Liouville equation near the horizon

Connects the symmetry generators to black hole microstates

Abstract

In this article we compute the black hole entropy by finding a classical central charge of the Virasoro algebra of a Liouville theory using the Cardy formula. This is done by performing a dimensional reduction of the Einstein Hilbert action with the ansatz of spherical symmetry and writing the metric in conformally flat form. We obtain two coupled field equations. Using the near horizon approximation the field equation for the conformal factor decouples. The one concerning the conformal factor is a Liouville equation, it posses the symmetry induced by a Virasoro algebra. We argue that it describes the microstates of the black hole, namely the generators of this symmetry do not change the thermodynamical properties of the black hole.