Abstract
The powerful approach to statistical mechanics proposed by Brown et al. is extended to the case in which the electromagnetic field is present as well as the gravitational field. We apply this formalism to investigate the ensemble dependence for the thermodynamic stability of systems containing a straight cosmic string passing through a charged black hole. While both the canonical pressure and grand canonical pressure ensembles are unstable, the equilibrium states of the grand microcanonical ensemble and the microcanonical pressure ensemble are always stable. The grand microcanonical pressure ensemble is stable only if the charge of the system is not too close to the critical charge of the black hole. The "stable" states of these ensembles may or may not spontaneously decay to a pure black hole. For all the four pressure ensembles, equilibrium states exist only when $0\ensuremath{\le}P\ensuremath{\le}\frac{1}{4}$, where $P$ is the canonical pressure. Using the entropy as the integration measure for the path-integral representations of partition functions, we examine the effects on various thermodynamic variables due to quantum fluctuations of the metric. We show that there are no corrections, due to the quantum fluctuations of the electric charge, to the thermodynamic properties of an isolated neutral hole-string system provided that the $\mathrm{CPT}$ theorem is valid.
Published Version
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