Thermodynamics of rotating solutions in (n+1)-dimensional Einstein-Maxwell-dilaton gravity

We construct a class of charged, rotating solutions of (n+1)-dimensional Einstein-Maxwell-dilaton gravity with cylindrical or toroidal horizons in the presence of Liouville-type potentials and investigate their properties. These solutions are neither asymptotically flat nor (anti)-de Sitter. We find that these solutions can represent black brane, with inner and outer event horizons, an extreme black brane or a naked singularity provided the parameters of the solutions are chosen suitably. We also compute temperature, entropy, charge, electric potential, mass and angular momentum of the black brane solutions, and find that these quantities satisfy the first law of thermodynamics. We find a Smarr-type formula and perform a stability analysis by computing the heat capacity in the canonical ensemble. We find that the system is thermally stable when the coupling constant between the dilaton and matter field alpha <= 1, while for alpha > 1 the system has an unstable phase. This shows that the dilaton field makes the solution unstable, while it is stable even in Lovelock gravity.