The First Law of Thermodynamics for Kerr-Anti-de Sitter Black Holes

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  • 30 August 2004
Abstract
We obtain expressions for the mass and angular momenta of rotating black holes in anti-de Sitter backgrounds in four, five and higher dimensions. We verify explicitly that our expressions satisfy the first law of thermodynamics, thus allowing an unambiguous identification of the entropy of these black holes with 1/4 of the area. We find that the associated thermodynamic potential equals the background-subtracted Euclidean action multiplied by the temperature. Our expressions differ from many given in the literature. We find that in more than four dimensions, only our expressions satisfy the first law of thermodynamics. We indicate the relevance of these results to the AdS/CFT correspondence.

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