Calculation of the entropy from the heat kernel in a spacetime with a conical singularity.

Abstract

The present Brief Report deals with some difficulties recently encountered when trying to reobtain the Susskind-Uglum entropy in a conically singular spacetime by heat-kernel expansion. As alternatives, smoothing the singularity, cutting it off, and conformally going to the (nonsingular) optical metric have been considered by several authors. Here, we show that by using mathematical results on singular manifolds and the orthodox definition of the heat kernel and $\ensuremath{\zeta}$ function a direct treatment of the conical singularity is possible. In particular, this can be done by applying standard $\ensuremath{\zeta}$-function regularization methods.