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

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.

Automated summary

In this study, an exact solution for the AdS black hole solution in Einstein-Gauss-Bonnet gravity coupled with nonlinear electrodynamics has been obtained. The thermodynamic properties of the obtained solution, including mass, temperature, entropy, heat capacity, and free energy, are investigated based on horizon thermodynamics. It is found that smaller nonsingular black holes are stable due to positive heat capacity and negative free energy. The relations between the black hole shadow and the critical behavior of charged EGB AdS regular black hole in the extended phase space are explicitly traced.