Thermodynamics of static black objects in D dimensional Einstein-Gauss-Bonnet gravity with D-4 compact dimensions

Abstract

We investigate the thermodynamics of static black objects such as black holes, black strings and their generalizations to D dimensions (`black branes') in a gravitational theory containing the four dimensional Gauss-Bonnet term in the action, when D-4 of the dimensions are compactified on a torus. The entropies of black holes and black branes are compared to obtain information on the stability of these objects and to find their phase diagrams. We demonstrate the existence of a critical mass, which depends on the scale of the compactified dimensions, below which the black hole entropy dominates over the entropy of the black membrane.

An error in the computation of entropy was corrected by properly taking into account the ADM mass, and the gravitational tension due to compactification. Verified that the results agree with the geometric entropy formula of Fursaev and Solodukhin. Conclusions remain unchanged

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