Thermodynamics of charged topological dilaton black holes

Abstract

A class of $(n+1)$-dimensional $(n\ensuremath{\ge}3)$ topological black hole solutions in Einstein-Maxwell-dilaton theory with Liouville-type potentials for the dilaton field is presented. In these spacetimes, the black hole horizon and the cosmological horizon can be an $(n\ensuremath{-}1)$-dimensional positive, zero, or negative constant curvature hypersurface. Because of the presence of the dilaton field, these topological black holes are neither asymptotically flat nor (anti--)de Sitter. We calculate the charge, mass, temperature, entropy, and electric potential of these solutions. We also analyze thermodynamics of these topological black holes and disclose the effect of the dilaton field on the thermal stability of the solutions.