2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/175362We 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.Revtex4, 23 pages. Minor typos corrected and one reference addedGeneral Relativity and Quantum CosmologyHigh Energy Physics - Theorytext