Horizon symmetries and hairy black holes in AdS

TL;DR

This paper explores the emergence of supertranslation symmetries in AdS black holes within massive 3D gravity, revealing infinite-dimensional symmetries at the boundary and horizon that relate to black hole entropy and higher-curvature effects.

Contribution

It demonstrates the presence of supertranslation symmetries and associated charges in AdS black holes in massive gravity, including their role in entropy and higher-curvature corrections.

Findings

Infinite-dimensional Virasoro symmetries at boundary and horizon.

Explicit computation of supertranslation charges.

Near horizon charges include higher-curvature corrections.

Abstract

We investigate whether supertranslation symmetry may appear in a scenario that involves black holes in AdS space. The framework we consider is massive 3D gravity, which admits a rich black hole phase space, including stationary AdS black holes with softly decaying hair. We consider a set of asymptotic conditions that permits such decaying near the boundary, and which, in addition to the local conformal symmetry, is preserved by an extra local current. The corresponding algebra of diffeomorphisms consists of two copies of Virasoro algebra in semi-direct sum with an infinite-dimensional Abelian ideal. We then reorient the analysis to the near horizon region, where infinite-dimensional symmetries also appear. The supertranslation symmetry at the horizon yields an infinite set of non-trivial charges, which we explicitly compute. The zero-mode of these charges correctly reproduces the black hole entropy. In contrast to Einstein gravity, in the higher-derivative theory subleading terms in the near horizon expansion contribute to the near horizon charges. Such terms happen to capture the higher-curvature corrections to the Bekenstein area law.