GEOMETRIC ENTROPY AND CURVATURE COUPLING IN CONICAL SPACES - ZETA-FUNCTION APPROACH

The local xi-function approach is implemented to regularize the natura l path integral definition of the geometric entropy in the large mass black hole Euclidean manifold. The case of a massless field coupled wi th the (off-shell) singular curvature is considered. It is proved that the geometric entropy is independent of the curvature coupling parame ter, xi, avoiding the negative values obtained in other approaches.