Thermodynamics of rotating black branes in $(n+1)$-dimensional Einstein-Born-Infeld gravity

TL;DR

This paper introduces new charged rotating black brane solutions in higher-dimensional Einstein-Born-Infeld gravity, analyzes their thermodynamic properties, and demonstrates their thermal stability across various parameters.

Contribution

It presents novel rotating black brane solutions in Einstein-Born-Infeld gravity with detailed thermodynamic analysis and stability assessment.

Findings

Solutions can represent black branes, extremal black branes, or naked singularities.

Thermodynamic quantities satisfy the first law and follow a Smarr-type relation.

The system is thermally stable in the entire phase space.

Abstract

We construct a new class of charged rotating solutions of $(n+1)$-dimensional Einstein-Born-Infeld gravity with cylindrical or toroidal horizons in the presence of cosmological constant and investigate their properties. These solutions are asymptotically (anti)-de Sitter and reduce to the solutions of Einstein-Maxwell gravity as the Born-Infeld parameters goes to infinity. We find that these solutions can represent black branes, with inner and outer event horizons, an extreme black brane or a naked singularity provided the parameters of the solutions are chosen suitably. We compute temperature, mass, angular momentum, entropy, charge and electric potential of the black brane solutions. We obtain a Smarr-type formula and show that these quantities satisfy the first law of thermodynamics. We also perform a stability analysis by computing the heat capacity and the determinant of Hessian matrix of mass with respect to its thermodynamic variables in both the canonical and the grand-canonical ensembles, and show that the system is thermally stable in the whole phase space.