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

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Thermodynamics of static black objects in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>D</mml:mi></mml:math>dimensional Einstein-Gauss-Bonnet gravity with<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>D</mml:mi><mml:mo>−</mml:mo><mml:mn>4</mml:mn></mml:math>compact dimensions

Thermodynamics of static black objects inDdimensional Einstein-Gauss-Bonnet gravity withD−4compact dimensions