Thermodynamics of Asymptotically Locally AdS Spacetimes

Details Thermodynamics of Asymptotically Locally AdS Spacetimes Thermodynamics of Asymptotically Locally AdS Spacetimes

2005-05-23

arxiv.org/abs/hep-th/0505190v3

JHEP0508:004,2005

Physics

High Energy Physics

High Energy Physics - Theory

55 pages; v2 one reference added, few signs corrected, version to appear in JHEP; v3 corrected minor typos and acknowledgement

Scientific paper

10.1088/1126-6708/2005/08/004

We formulate the variational problem for AdS gravity with Dirichlet boundary conditions and demonstrate that the covariant counterterms are necessary to make the variational problem well-posed. The holographic charges associated with asymptotic symmetries are then rederived via Noether's theorem and `covariant phase space' techniques. This allows us to prove the first law of black hole mechanics for general asymptotically locally AdS black hole spacetimes. We illustrate our discussion by computing the conserved charges and verifying the first law for the four dimensional Kerr-Newman-AdS and the five dimensional Kerr-AdS black holes.

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