Thermodynamics of rotating black branes in Gauss-Bonnet-Born-Infeld gravity

Considering both the Gauss-Bonnet and the Born-Infeld terms, which are on a similar footing with regard to the string corrections on the gravity and electrodynamics sides respectively, we present a new class of rotating solutions in Gauss-Bonnet-Born-Infeld gravity with k rotation parameters. Although these solutions are not real in the whole space-time, they can be made real by a suitable transformation. Depending on the metric parameters, these real solutions may be interpreted as black brane solutions with inner and outer event horizons, an extreme black brane or naked singularity. We calculate the finite action and conserved quantities of the solutions by using the counterterm method, and find that these quantities do not depend on the Gauss-Bonnet parameter. We also compute the temperature, the angular velocities, the electric charge and the electric potential. Then, we calculate the entropy of the black brane through the use of the Gibbs-Duhem relation and show that it obeys the area law of entropy. We obtain a Smarr-type formula for the mass as a function of the entropy, the angular momenta and the charge, and show that the conserved and thermodynamic quantities satisfy the first law of thermodynamics. Finally, we perform a stability analysis in both the canonical and the grand-canonical ensemble and show that the presence of a nonlinear electromagnetic field has no effect on the stability of the black branes, which are stable in the whole phase space.