Thermodynamics of third order Lovelock adS black holes in the presence of Born-Infeld type nonlinear electrodynamics

TL;DR

This paper explores the thermodynamics and stability of topological black holes in third order Lovelock gravity coupled with nonlinear Born-Infeld electrodynamics in anti-de Sitter space, including extended phase space analysis.

Contribution

It provides new solutions and thermodynamic analysis of Lovelock-AdS black holes with nonlinear electrodynamics, extending previous studies to include stability and phase space thermodynamics.

Findings

Black hole solutions with specific thermodynamic properties.

Verification of the first law of thermodynamics for these solutions.

Analysis of thermal stability via heat capacity and Hessian determinant.

Abstract

In this paper, we obtain topological black hole solutions of third order Lovelock gravity couple with two classes of Born-Infeld type nonlinear electrodynamics with anti-de Sitter asymptotic structure. We investigate geometric and thermodynamics properties of the solutions and obtain conserved quantities of the black holes. We examine the first law of thermodynamics and find that the conserved and thermodynamic quantities of the black hole solutions satisfy the first law of thermodynamics. Finally, we calculate the heat capacity and determinant of Hessian matrix to evaluate thermal stability in both canonical and grand canonical ensembles. Moreover, we consider extended phase space thermodynamics to obtain generalized first law of thermodynamics as well as extended Smarr formula.