Black Hole Entropy and Soft Hair

Abstract

A set of infinitesimal $\mathrm{Virasor}{\mathrm{o}}_{\mathrm{L}}\otimes \mathrm{Virasor}{\mathrm{o}}_{\mathrm{R}}$ 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.

Accepted for publication by JHEP on 05/12/18