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

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.

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

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