Topological Black Holes in Lovelock-Born-Infeld Gravity

TL;DR

This paper explores topological black holes in third order Lovelock gravity with Born-Infeld electromagnetic fields, analyzing their thermodynamics, stability, and geometric properties, revealing that nonlinear fields and higher curvature terms do not affect their stability.

Contribution

It introduces new topological black hole solutions in Lovelock-Born-Infeld gravity and thoroughly investigates their thermodynamic behavior and stability properties.

Findings

Black holes can have inner/outer horizons, be extremal, or naked singularities.

Thermodynamics satisfies the first law, and entropy follows the area law.

Black branes remain stable despite nonlinear electromagnetic and higher curvature effects.

Abstract

In this paper, we present topological black holes of third order Lovelock gravity in the presence of cosmological constant and nonlinear electromagnetic Born-Infeld field. Depending on the metric parameters, these solutions may be interpreted as black hole solutions with inner and outer event horizons, an extreme black hole or naked singularity. We investigate the thermodynamics of asymptotically flat solutions and show that the thermodynamic and conserved quantities of these black holes satisfy the first law of thermodynamic. We also endow the Ricci flat solutions with a global rotation and calculate the finite action and conserved quantities of these class of solutions by using the counterterm method. We compute the entropy through the use of the Gibbs-Duhem relation and find that the entropy obeys the area law. We obtain a Smarr-type formula for the mass as a function of the entropy, the angular momenta, and the charge, and compute temperature, angular velocities, and electric potential and show that these thermodynamic quantities coincide with their values which are computed through the use of geometry. Finally, we perform a stability analysis for this class of solutions in both the canonical and the grand-canonical ensemble and show that the presence of a nonlinear electromagnetic field and higher curvature terms has no effect on the stability of the black branes, and they are stable in the whole phase space.