Geometrothermodynamics of black holes in Lovelock gravity with a nonlinear electrodynamics

TL;DR

This paper investigates the phase transitions of AdS black holes in Lovelock gravity with nonlinear electrodynamics, analyzing thermodynamic stability through heat capacity and Ricci scalar, and comparing geometric and thermodynamic singularities.

Contribution

It introduces new black hole solutions in Lovelock gravity with nonlinear electrodynamics and applies geometrothermodynamics to analyze phase transitions and stability.

Findings

Correlation between Ricci scalar singularities and heat capacity zeros.

Lovelock gravity and nonlinear electrodynamics significantly affect phase transition points.

Comparison of geometric and thermodynamic methods for phase transition analysis.

Abstract

The objective of the present paper is to analyze the phase transition of asymptotically anti-de Sitter (AdS) black hole solutions in Lovelock gravity in the presence of nonlinear electrodynamics. First, we present the asymptotically AdS black hole solutions for two classes of the Born-Infeld type of nonlinear electrodynamics coupled with Einstein, Gauss-Bonnet and third order Lovelock gravity, separately. Then, in order to discuss the phase transition, we calculate both the heat capacity and the Ricci scalar of the thermodynamical line element. We present a comparison between the singular points of the Ricci scalar using Geometrothermodynamics method and the corresponding vanishing points of the heat capacity in the canonical ensemble. In addition, we discuss the effects of both Lovelock and nonlinear electrodynamics on the phase transition points.