Mechanics of higher-dimensional black holes in asymptotically anti-de Sitter space-times

TL;DR

This paper develops a covariant phase space framework for higher-dimensional black holes in asymptotically anti-de Sitter space-times, deriving a local first law of black hole mechanics applicable without global stationarity assumptions.

Contribution

It introduces a covariant phase space approach for Einstein gravity with negative cosmological constant in higher dimensions, generalizing black hole mechanics laws to local horizons.

Findings

Derived a local first law of black hole mechanics for AdS black holes.

Connected the general first law to the specific Kerr-AdS case.

Established a framework for analyzing black holes in asymptotically AdS space-times.

Abstract

We construct a covariant phase space for Einstein gravity in dimensions d>=4 with negative cosmological constant, describing black holes in local equilibrium. Thus, space-times under consideration are asymptotically anti-de Sitter and admit an inner boundary representing an isolated horizon. This allows us to derive a first law of black hole mechanics that involves only quantities defined quasi-locally at the horizon, without having to assume that the bulk space-time is stationary. The first law proposed by Gibbons et al. for the Kerr-AdS family follows from a special case of this much more general first law.