Entropy and topology for gravitational instantons

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 = χA/8, is obtained. This formula provides the correct results for a wide class of gravitational instantons described by both spherically and axially symmetric metrics. PACS: 04.70.Dy, 04.20.Gz, 04.62.+v Typeset using REVTEX ∗Electronic address: [email protected] †Electronic address: [email protected] 1