Thermodynamics of rotating black branes in Einstein-Born-Infeld-dilaton gravity

In this paper, we construct a new class of charged, rotating solutions for (n + 1)-dimensional Einstein - Born - Infeld-dilaton gravity with Liouville-type potentials and investigate their properties. These solutions are neither asymptotically. at nor (anti-) de Sitter. We find that these solutions can represent a 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 the temperature, entropy, charge, electric potential, mass and angular momentum of the black brane solutions, and show that these quantities satisfy the first law of thermodynamics. We find that the conserved quantities are independent of the Born - Infeld parameter beta, while they do depend on the dilaton coupling constant alpha. We also find the total mass of the black brane with infinite boundary as a function of the entropy, the angular momenta and the charge and perform a stability analysis by computing the heat capacity in the canonical ensemble. We find that the system is thermally stable for alpha <= 1 independently of the values of the charge and Born - Infeld parameters, while for alpha > 1 the system has an unstable phase. In the latter case, the solutions are stable provided alpha <= alpha(max) and beta >= beta(min), where alpha(max) and beta(min) depend on the charge and the dimensionality of the spacetime. That is, the solutions are unstable for a highly non-linear electromagnetic field or when the dilaton coupling constant is large.