Charged rotating black branes in anti–de Sitter Einstein-Gauss-Bonnet gravity

We present a new class of charged rotating solutions in the Einstein-Gauss-Bonnet gravity with a negative cosmological constant. These solutions may be interpreted as black brane solutions with two inner and outer event horizons or an extreme black brane depending on the value of the mass parameter m. We also find that the Killing vectors are the null generators of the event horizon. The physical properties of the brane such as the temperature, the angular velocity, the entropy, the electric charge and potential are computed. We also compute the action and the Gibbs potential as a function of temperature and angular velocity for the uncharged solutions, and compute the angular momentum and the mass of the black brane through the use of the Gibbs potential. We show that these thermodynamic quantities satisfy the first law of thermodynamics. We also perform a local stability analysis of the asymptotically anti--de Sitter (AdS) uncharged rotating black brane in various dimensions and show that they are locally stable for the whole phase space both in the canonical and grand-canonical ensemble. We find that the thermodynamic properties of Gauss-Bonnet rotating black branes are completely the same as those without the Gauss-Bonnet term, although the two solutions are quite different.