Black Hole Entropy and Soft Hair

TL;DR

The paper identifies a nontrivial Virasoro action on the Kerr black hole horizon, derived from hidden conformal symmetry in the near-horizon phase space. Using the covariant phase space formalism, it shows that a Wald-Zoupas counterterm is needed to obtain a well-defined, associative charge algebra, yielding central charges $c_L=c_R=12J$. Assuming a quantum Hilbert space where these charges act and the Cardy formula applies, the resulting microscopic degeneracies reproduce the macroscopic Kerr area law $S_{ m BH}=rac{ ext{Area}}{4}$. This work provides incremental evidence that horizon degrees of freedom organized by horizon Virasoro symmetries can account for black hole entropy and offers perspective on information-theoretic aspects of black holes.

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.