Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2000-11-20
Phys.Rev. D63 (2001) 084013
Physics
High Energy Physics
High Energy Physics - Theory
Revtex, 16 pages, no figures. Minor changes. Version accepted for publication in Phys. Rev. D
Scientific paper
10.1103/PhysRevD.63.084013
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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