Thermodynamic analysis of topological black holes in Gauss-Bonnet gravity with nonlinear source

TL;DR

This paper explores the thermodynamics and stability of topological black holes in Gauss-Bonnet gravity with nonlinear electrodynamics, revealing singularities, thermodynamic behaviors, and conditions for stability.

Contribution

It introduces new topological black hole solutions in Gauss-Bonnet gravity with nonlinear sources and analyzes their thermodynamic and stability properties.

Findings

Identified intrinsic singularities at the origin of the solutions.

Derived thermodynamic quantities and confirmed the first law of thermodynamics.

Established stability conditions based on heat capacity and horizon radius.

Abstract

Employing two classes of nonlinear electrodynamics, we obtain topological black hole solutions of Gauss-Bonnet gravity. We investigate geometric properties of the solutions and find that there is an intrinsic singularity at the origin. We investigate the thermodynamic properties of the asymptotically flat black holes and also asymptotically adS solutions. Using suitable local transformation, we generalize static horizon-flat solutions to rotating ones. We discuss their conserved and thermodynamic quantities as well as the first law of thermodynamics. Finally, we calculate the heat capacity of the solutions to obtain a constraint on the horizon radius of stable solutions.