4D Einstein–Gauss–Bonnet Gravity Coupled with Nonlinear Electrodynamics

A new exact spherically symmetric and magnetically charged black hole solution in regularization scheme of Glavan and Lin is obtained. The nonlinear electrodynamics Lagrangian is given by LNED=−F/(1+2βF4), where F is the field invariant. We study the thermodynamics calculating the Hawking temperature and the heat capacity of the black hole. The phase transitions take place when the Hawking temperature has an extremum and the heat capacity is singular. We demonstrate that black holes are thermodynamically stable in some range of event horizon radii where the heat capacity is positive. The BH shadow radius is calculated and we study its dependance on model parameters