Thermodynamic instability of topological black holes in Gauss-Bonnet gravity with a generalized electrodynamics

TL;DR

This paper studies the thermodynamic stability of higher-dimensional topological black holes in Gauss-Bonnet gravity with generalized electrodynamics, revealing how nonlinear electrodynamics influences their thermodynamic behavior.

Contribution

It introduces quadratic Maxwell invariant corrections to Gauss-Bonnet gravity and analyzes the resulting black hole solutions' thermodynamics and stability in various asymptotic regimes.

Findings

Conserved quantities satisfy the first law of thermodynamics.

Thermodynamic stability depends on nonlinear electrodynamics effects.

Instability criteria are established for different ensembles.

Abstract

Motivated by the string corrections on the gravity and electrodynamics sides, we consider a quadratic Maxwell invariant term as a correction of the Maxwell Lagrangian to obtain exact solutions of higher dimensional topological black holes in Gauss-Bonnet gravity. We first investigate the asymptotically flat solutions and obtain conserved and thermodynamic quantities which satisfy the first law of thermodynamics. We also analyze thermodynamic stability of the solutions by calculating the heat capacity and the Hessian matrix. Then, we focus on horizon-flat solutions with adS asymptote and produce a rotating spacetime with a suitable transformation. In addition, we calculate the conserved and thermodynamic quantities for asymptotically adS black branes which satisfy the first law of thermodynamics. Finally, we perform thermodynamic instability criterion to investigate the effects of nonlinear electrodynamics in canonical and grand canonical ensembles.