Thermodynamics of asymptotically flat charged black holes in third order Lovelock gravity

Abstract

We present a new class of asymptotically flat charge static solutions in third order Lovelock gravity. These solutions present black hole solutions with two inner and outer event horizons, extreme black holes, or naked singularities provided the parameters of the solutions are chosen suitable. We find that the uncharged asymptotically flat solutions can present black holes with two inner and outer horizons. This kind of solution does not exist in Einstein or Gauss-Bonnet gravity, and it is a special effect in third order Lovelock gravity. We compute temperature, entropy, charge, electric potential, and mass of the black hole solutions, and find that these quantities satisfy the first law of thermodynamics. We also perform a stability analysis by computing the determinant of the Hessian matrix of the mass with respect to its thermodynamic variables in both the canonical and the grand-canonical ensembles, and show that there exists only an intermediate stable phase.