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

Abstract

The local $ζ-$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 $ξ$ avoiding negative values obtained in other approaches.