Black hole entropy and thermodynamics from symmetries

TL;DR

This paper develops a systematic method to compute black hole entropy using boundary symmetries and Virasoro algebra charges, successfully reproducing the area law for various black holes and recovering the first law of thermodynamics.

Contribution

The paper introduces a new approach to calculate black hole entropy from boundary symmetries, fixing the zero mode normalization automatically, and applies it to BTZ and Kerr-AdS4 black holes.

Findings

Reproduces the Bekenstein-Hawking entropy with correct factor

Derives the first law of black hole thermodynamics within the framework

Provides a consistent method to compute Virasoro charges from boundary symmetries

Abstract

Given a boundary of spacetime preserved by a Diff(S^{1}) sub-algebra, we propose a systematic method to compute the zero mode and the central extension of the associated Virasoro algebra of charges. Using these values in the Cardy formula, we may derive an associated statistical entropy to be compared with the Bekenstein-Hawking result. To illustrate our method, we study in detail the BTZ and the rotating Kerr-adS_{4} black holes (at spatial infinity and on the horizon). In both cases, we are able to reproduce the area law with the correct factor of 1/4 for the entropy. We also recover within our framework the first law of black hole thermodynamics. We compare our results with the analogous derivations proposed by Carlip and others. Although similar, our method differs in the computation of the zero mode. In particular, the normalization of the ground state is automatically fixed by our construction.