Entropy and Topology for Gravitational Instantons

TL;DR

This paper establishes a direct relation between topology and thermodynamics of gravitational instantons, proposing a new entropy formula linking Euler characteristic and area, which aligns with known results across various instanton classes.

Contribution

It introduces a novel formulation of the Bekenstein-Hawking entropy relation connecting Euler characteristic and area for gravitational instantons.

Findings

Derived a new entropy formula: S=χA/8.

Validated the formula across spherically and axially symmetric instantons.

Linked topological invariants with thermodynamic properties in gravity.

Abstract

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.