Entropy and topology for manifolds with boundaries

Details Entropy and topology for manifolds with boundaries Entropy and topology for manifolds with boundaries

1995-09-15

arxiv.org/abs/hep-th/9509093v3

Nucl.Phys.Proc.Suppl. 57 (1997) 197-200

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, phyzzx, no figures

Scientific paper

In this work a deep relation between topology and thermodynamical features of manifolds with boundaries is shown. The expression for the Euler characteristic, through the Gauss- Bonnet integral, and the one for the entropy of gravitational instantons are proposed in a form which makes the relation between them self-evident. A generalization of Bekenstein-Hawking formula, in which entropy and Euler characteristic are related in the form $S=\chi A/8$, is obtained. This formula reproduces the correct result for extreme black hole, where the Bekenstein-Hawking one fails ($S=0$ but $A \neq 0$). In such a way it recovers a unified picture for the black hole entropy law. Moreover, it is proved that such a relation can be generalized to a wide class of manifolds with boundaries which are described by spherically symmetric metrics (e.g. Schwarzschild, Reissner-Nordstr\"{o}m, static de Sitter).

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