Supertranslations and Superrotations at the Black Hole Horizon

TL;DR

The paper shows that nonextremal black holes possess an infinite-dimensional near-horizon symmetry extending supertranslations with superrotations, realized as a semidirect product of Virasoro and an Abelian current. Using horizon-appropriate boundary conditions and covariant charges, the authors derive closed algebras in 3D and 4D, with zero modes reproducing key thermodynamic quantities: entropy times temperature and angular momentum for BTZ and Kerr, respectively. This work links horizon holography to BMS-like structures, offering a framework to explore central extensions and memory effects in black hole physics and suggesting directions for further study in extremal limits and alternative boundary conditions.

Abstract

We show that the asymptotic symmetries close to nonextremal black hole horizons are generated by an extension of supertranslations. This group is generated by a semidirect sum of Virasoro and Abelian currents. The charges associated with the asymptotic Killing symmetries satisfy the same algebra. When considering the special case of a stationary black hole, the zero mode charges correspond to the angular momentum and the entropy at the horizon.