Topological black holes in Lovelock-Born-Infeld gravity

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. *

Thermodynamics of Third Order Lovelock—Born—Infeld Black Holes

“…(12). The Hawking temperature of black holes on the outer horizon radius r + can be easily obtained by [30] T + = f ′ (r + ) 4π…”

Extended phase space of AdS black holes in Einstein–Gauss–Bonnet gravity with a quadratic nonlinear electrodynamics

“…Coupling of NED with the gravity was first done by Hoffmann [19]. The effects of Born-Infeld NED coupled to the gravitational field have been studied in various contexts such as superconductors [20], wormholes [21,22], static black holes [23] and rotating black objects [24]. In addition, another motivation for considering BornInfeld NED comes from the fact that it naturally arises in the low-energy limit of the heterotic string theory [25].…”

Third order Lovelock black branes in the presence of a nonlinear electromagnetic field

“…Hoffmann was a hendi@shirazu.ac.ir the first one to attempt to couple the nonlinear electrodynamics with gravity [17]. One of the current interesting subjects in black hole physics is the investigation of the effects of nonlinear electrodynamic fields on the gravitational field [18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37]. Considering nonlinear model of electrodynamic fields provide a powerful laboratory to analyze the properties of the black hole solutions.…”