Thermodynamics of Rotating Black Branes in Gauss-Bonnet-Born-Infeld Gravity

Abstract

Considering both the Gauss-Bonnet and the Born-Infeld terms, which are on similar footing with regard to string corrections on the gravity side and electrodynamic side, we present a new class of rotating solutions in Gauss-Bonnet gravity with $k$ rotation parameters in the presence of a nonlinear electromagnetic field. These solutions, which are asymptotically anti-de Sitter in the presence of cosmological constant, may be interpreted as black brane solutions with inner and outer event horizons, an extreme black brane or naked singularity provided the metric parameters are chosen suitably. 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 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 grand-canonical ensemble and show that the presence of a nonlinear electromagnetic field has no effect on the stability of the black branes, and they are stable in the whole phase space.

17 pages, one figure

References in corpus (7)

• Thermodynamics of Rotating Charged Black Branes in Third Order Lovelock Gravity and the Counterterm Method
• Taub-NUT/Bolt Black Holes in Gauss-Bonnet-Maxwell Gravity
• Thermodynamics of rotating solutions in (n+1)-dimensional Einstein-Maxwell-dilaton gravity
• Counterterm Method in Lovelock Theory and Horizonless Solutions in Dimensionally Continued Gravity
• Thermodynamics of rotating black branes in $(n+1)$-dimensional Einstein-Born-Infeld gravity
• Thermodynamics of Rotating Solutions in Gauss-Bonnet-Maxwell Gravity and the Counterterm Method
• Features of gravity-Yang-Mills hierarchies in d-dimensions

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