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

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, with $D\ensuremath{-}4$ dimensions compactified 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.

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