Black hole and black brane solutions in R⁴ x (S¹)ⁿ spaces

We study black hole and black brane solutions in brane theories with flat extra dimensions in Einstein gravity. Black hole solutions are found using an expansion in the ratio of the radius of the horizon, m, and the circumference of the compact dimension, L. We also 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.