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

Abstract

The local $\hat{I}\P -$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 $\hat{I}¾$ avoiding negative values obtained in other approaches.

6 pages, LaTex, no figures, minor text errors corrected, a reference added, final version to be published in Class. Quant. Grav