Holographic Stress Tensors for Kerr-AdS Black Holes

Abstract

We use the counterterm subtraction method to calculate the action and stress-energy-momentum tensor for the (Kerr) rotating black holes in AdS_{n+1}, for n=2, 3 and 4. We demonstrate that the expressions for the total energy for the Kerr-AdS_3 and Kerr-AdS_5 spacetimes, in the limit of vanishing black hole mass, are equal to the Casimir energies of the holographically dual n-dimensional conformal field theories. In particular, for Kerr-AdS_5, dual to the case of four dimensional N=4 supersymmetric Yang-Mills theory on the rotating Einstein universe, we explicitly verify the equality of the zero mass stress tensor from the two sides of the correspondence, and present the result for general mass as a prediction from gravity. Amusingly, it is observed in four dimensions that while the trace of the stress tensor defined using the standard counterterms does not vanish, its integral does, thereby keeping the action free of ultraviolet divergences. Using a different regularisation scheme another stress tensor can be defined, which is traceless.

9 pages, RevTeX; v5: Note added (as in published PRD version) about the new stress tensor not having same conserved quantities as old. i.e., "improvement" fails. The fascinating reason will be reported on in a separate publication.)

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• Thermodynamics of Kerr-Newman-AdS Black Holes and Conformal Field Theories
• Holography, Thermodynamics and Fluctuations of Charged AdS Black Holes
• The Gravitational Action in Asymptotically AdS and Flat Spacetimes
• Charged and rotating AdS black holes and their CFT duals
• Misner String Entropy
• AdS/CFT Duals of Topological Black Holes and the Entropy of Zero-Energy States
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• Entropy of Rotating Misner String Spacetimes
• Holography and Rotating AdS Black Holes
• The Free Energy of N=4 Super-Yang-Mills and the AdS/CFT Correspondence

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