Thermodynamic properties, thermal image and phase transition of Einstein-Gauss-Bonnet black hole coupled with nonlinear electrodynamics

TL;DR

This paper presents an exact $AdS$ black hole solution in Einstein-Gauss-Bonnet gravity coupled with nonlinear electrodynamics, analyzing its thermodynamic behavior, phase transitions, stability, and black hole shadow relations.

Contribution

It introduces a new exact black hole solution in EGB gravity with nonlinear electrodynamics and explores its thermodynamic and phase transition properties.

Findings

Maximum Hawking temperature at phase transition point

Small black holes are thermodynamically stable

Black hole shadow correlates with critical behavior

Abstract

We obtain an exact solution of $AdS$ black hole solution in Einstein-Gauss-Bonnet (EGB) gravity coupled with nonlinear electrodynamics. It interpolates with the $AdS$ regular black hole and $AdS$ EGB black hole in the absence of the Gauss-Bonnet coupling constant and both magnetic monopole charge and deviation parameter, respectively. Based on horizon thermodynamics, we study the thermodynamic properties of the obtained solution (e.g. mass, temperature, entropy, heat capacity and free energy). The Hawking temperature of the nonsingular black hole gets the maximum value at the point where specific heat diverges and the second-order phase transition occurs at the same point. We find that the smaller nonsingular black holes are stable due to positive heat capacity and negative free energy. We explicitly trace the relations between the black hole shadow and the critical behavior of charged EGB $AdS$ regular black hole in the extended phase space.