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

arXiv commentRevtex4, 23 pages. Minor typos corrected and one reference added

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• New Variables for Classical and Quantum Gravity in all Dimensions V. Isolated Horizon Boundary Degrees of Freedom
• Action and Hamiltonians in higher dimensional general relativity: First order framework
• Isolated horizons in higher-dimensional Einstein-Gauss-Bonnet gravity
• Supersymmetric isolated horizons in ADS spacetime
• The Wald entropy formula and loop quantum gravity
• Barbero-Immirzi parameter, manifold invariants and Euclidean path integrals
• Energy in higher-dimensional spacetimes
• The Entropy of Higher Dimensional Nonrotating Isolated Horizons from Loop Quantum Gravity
• The thermodynamics of isolated horizons in loop quantum gravity
• Supersymmetric isolated horizons
• Neighbourhoods of Isolated Horizons and their stationarity
• Isolated horizons, p-form matter fields, topology and the black-hole/string correspondence principle
• A note on the mass of Kerr-AdS black holes in the off-shell generalized ADT formalism