Geometrothermodynamics of black holes in Lovelock gravity with a nonlinear electrodynamics

Understand

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.