Central Charges for AdS Black Holes

TL;DR

This paper explores how adding a negative cosmological constant to Kerr black holes in AdS space introduces a Virasoro algebra with a central charge, linking horizon symmetries to black hole entropy via the Cardy formula.

Contribution

It extends the concept of horizon symmetries and soft hair to Kerr-AdS black holes, deriving a central charge and connecting it to the Bekenstein-Hawking entropy.

Findings

Identification of a Virasoro algebra with a central charge for Kerr-AdS horizons

Derivation of a boundary counterterm ensuring well-defined charges

Confirmation that the entropy matches the area law via the Cardy formula

Abstract

Nontrivial diffeomorphisms act on the horizon of a generic 4D black holes and create distinguishing features referred to as soft hair. Amongst these are a left-right pair of Virasoro algebras with associated charges that reproduce the Bekenstein-Hawking entropy for Kerr black holes. In this paper we show that if one adds a negative cosmological constant, there is a similar set of infinitesimal diffeomorphisms that act non-trivially on the horizon. The algebra of these diffeomorphisms gives rise to a central charge. Adding a boundary counterterm, justified to achieve integrability, leads to well-defined central charges with cL = cR. The macroscopic area law for Kerr-AdS black holes follows from the assumption of a Cardy formula governing the black hole microstates.