Black Hole Entropy and Soft Hair

TL;DR

This paper identifies a set of Virasoro symmetries acting on Kerr black hole horizons, computes their charges, and shows these reproduce the black hole entropy via the Cardy formula, linking horizon symmetries to entropy.

Contribution

It introduces a new set of horizon symmetries for Kerr black holes, computes their charges with necessary counterterms, and connects these to the entropy through the Cardy formula.

Findings

Virasoro charges are computed as horizon surface integrals.

Central charges are found to be c_L=c_R=12J.

The entropy matches the Bekenstein-Hawking area law.

Abstract

A set of infinitesimal ${\rm Virasoro_{\,L}}\otimes{\rm Virasoro_{\,R}}$ diffeomorphisms are presented which act non-trivially on the horizon of a generic Kerr black hole with spin J. The covariant phase space formalism provides a formula for the Virasoro charges as surface integrals on the horizon. Integrability and associativity of the charge algebra are shown to require the inclusion of `Wald-Zoupas' counterterms. A counterterm satisfying the known consistency requirement is constructed and yields central charges $c_L=c_R=12J$. Assuming the existence of a quantum Hilbert space on which these charges generate the symmetries, as well as the applicability of the Cardy formula, the central charges reproduce the macroscopic area-entropy law for generic Kerr black holes.