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

TL;DR

This paper introduces new rotating black brane solutions in Gauss-Bonnet gravity with nonlinear electromagnetic fields, analyzing their thermodynamics, stability, and confirming they obey the first law of thermodynamics.

Contribution

It presents novel rotating black brane solutions with nonlinear electromagnetic fields in Gauss-Bonnet gravity and examines their thermodynamic properties and stability.

Findings

Finite action and conserved quantities are independent of Gauss-Bonnet parameter.

Entropy obeys the area law and satisfies the first law of thermodynamics.

Black branes are stable across the entire phase space regardless of electromagnetic nonlinearity.

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.