Geometric Entropy and Curvature Coupling in Conical Spaces: zeta Function Approach

TL;DR

This paper uses the local zeta-function method to regularize geometric entropy in black hole Euclidean manifolds, showing it is independent of curvature coupling and avoiding negative entropy values.

Contribution

It introduces a zeta-function approach to compute geometric entropy, demonstrating independence from curvature coupling in singular curvature scenarios.

Findings

Entropy regularized via zeta-function method

Entropy independent of curvature coupling parameter ξ

Avoids negative entropy values in calculations

Abstract

The local $\zeta-$function approach is implemented to regularize the natural path integral definition of the geometric entropy in the large mass black hole Euclidean manifold. The case of a massless field coupled with the (off-shell) singular curvature is considered. It is proved that the geometric entropy is independent of the curvature coupling parameter $\xi$ avoiding negative values obtained in other approaches.