Einstein-Gauss-Bonnet gravity with nonlinear electrodynamics

TL;DR

This paper derives an exact magnetically charged black hole solution in 4D Einstein-Gauss-Bonnet gravity coupled with nonlinear electrodynamics, analyzing its thermodynamics, stability, and observational features like shadow radius and quasinormal modes.

Contribution

It presents a novel exact black hole solution in 4D Einstein-Gauss-Bonnet gravity with nonlinear electrodynamics and explores its thermodynamic and stability properties.

Findings

Black holes are thermodynamically stable within certain radii.

Logarithmic correction to entropy mimics quantum effects.

Black hole shadow radius depends on model parameters.

Abstract

We obtain an exact spherically symmetric and magnetically charged black hole solution in 4D Einstein-Gauss-Bonnet gravity coupled with nonlinear electrodynamics with the Lagrangian ${\cal L}_{NED} = -{\cal F}/(1+\sqrt{2\mid\beta{\cal F}\mid})$ (${\cal F}$ is the field strength invariant). The thermodynamics of the black hole is studied within our model. We calculate the Hawking temperature and the heat capacity of the black hole. The phase transitions occur in the point where the Hawking temperature possesses an extremum and the heat capacity diverges. It was shown that black holes are thermodynamically stable in some range of event horizon radii when the heat capacity and Hawking temperature are positive. The logarithmic correction to the Bekenstein - Hawking BH entropy is obtained which mimics a quantum correction. The dependence of the BH shadow radius on the model parameters is studied. We also investigate the particle emission rate of the BH. The stability of the BH is studied by analysing the quasinormal modes.