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

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.