Einstein-Gauss-Bonnet gravity with rational nonlinear electrodynamics

We obtain an exact spherically symmetric and magnetically charged black hole solution in 4D Einstein-Gauss-Bonnet gravity coupled with rational nonlinear electrodynamics. The thermodynamics of our model is studied. 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. We show that black holes are thermodynamically stable at some range of event horizon radii when the heat capacity is positive. The logarithmic correction to the Bekenstein-Hawking entropy is obtained.