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Renormalized black hole entropy in anti-de Sitter space via the "brick wall" method

Elizabeth Winstanley
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Abstract

We consider the entropy of a quantum scalar field on a background black hole geometry in asymptotically anti-de Sitter space-time, using the ``brick wall'' approach. In anti-de Sitter space, the theory has no infra-red divergences, and all ultra-violet divergences can be absorbed into a renormalization of the coupling constants in the one-loop effective gravitational Lagrangian. We then calculate the finite renormalized entropy for the Schwarzschild-anti-de Sitter and extremal Reissner-Nordstrom-anti-de Sitter black holes, and show that, at least for large black holes, the entropy is entirely accounted for by the one-loop Lagrangian, apart possibly from terms proportional to the logarithm of the event horizon radius. For small black holes, there are indications that non-perturbative quantum gravity effects become important.

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Elizabeth Winstanley. 2001-01-29. Renormalized black hole entropy in anti-de Sitter space via the "brick wall" method. https://doi.org/10.1103/physrevd.63.084013

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