Entropy and Topology for Gravitational Instantons

Details Entropy and Topology for Gravitational Instantons Entropy and Topology for Gravitational Instantons

1997-08-04

arxiv.org/abs/hep-th/9708014v1

Phys.Rev.D56:6458-6466,1997

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, RevTeX, accepted for publication in Phys. Rev. D

Scientific paper

10.1103/PhysRevD.56.6458

In this work a relation between topology and thermodynamical features of gravitational instantons 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 that makes the relation between them self-evident. A new formulation of the Bekenstein-Hawking formula, where the entropy and the Euler characteristic are related by $S=\chi A/8$, is obtained. This formula provides the correct results for a wide class of gravitational instantons described by both spherically and axially symmetric metrics.

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