Gravitational Thermodynamics of Schwarzschild-de Sitter Space
arXiv:hep-th/0203258
Abstract
The Euclidean Schwarzschild-de Sitter geometry may be considered as an extremum of two different action principles. If the thermodynamical parameters are held fixed at the cosmological horizon, one deals with the gravitational thermodynamical effects of the black hole but ignores those of the cosmological horizon. Conversely, if the macroscopical variables are held fixed at the black hole horizon, it is only the cosmological horizon thermodynamics which is dealt with. Both cases are analyzed. In particular, the internal energy U is calculated in the semiclassical approximation as a function of the mass parameter m of Schwarzschild de Sitter space. In the first case one finds U=+m, while in the second one gets U=-m. This suggests that de Sitter space is thermodynamically unstable under black hole formation.
arXiv comment10 pages. To be published in the proceedings of the Francqui Colloquium "Strings and Gravity: Tying the Forces Together", Brussels, October 19 - 21, 2001. Edited by Marc Henneaux and Alexander Sevrin
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