Extended Symmetries at Black Hole Horizons in Generic Dimensions

TL;DR

This paper demonstrates that BMS-like asymptotic symmetries are a universal feature of black hole horizons across all dimensions, with specific algebraic structures and links to black hole entropy and angular momentum.

Contribution

It generalizes the existence of horizon symmetries to arbitrary dimensions and connects these symmetries to physical properties like entropy and angular momentum.

Findings

BMS-like symmetries exist in all dimensions for black hole horizons.

The symmetry algebra includes supertranslations and generalized superrotations.

Surface charges relate to black hole entropy and angular momentum.

Abstract

Recently it has been shown that there is asymptotic BMS-like symmetry associated with the near-horizon geometry of black holes in three and four dimensions. In this paper, we show that the presence of such BMS-like symmetry is a ubiquitous feature for black holes in generic dimensions. For black holes in $D$ dimensions, the symmetry contains 2 supertranslations and $D-2$ generalized superrotations. The superrotations are found to generate a generalized Witt-like algebra that was previously noticed in a rather different construction. In the case of stationary and axisymmetric black holes, we calculate the surface charges and show that the zero-mode charges are intimately related to the entropy and angular momenta of the black hole.