Charged black holes in 4D Einstein–Gauss–Bonnet gravity coupled to nonlinear electrodynamics with maximum allowable symmetries

Recently a new model of nonlinear Maxwell electrodynamics which preserves both conformal and SO(2) duality-rotational invariance has been proposed. In this work, we consider this model as a source of gravitational field and study black holes of novel four-dimensional Einstein–Gauss–Bonnet gravity. In this framework we solve the gravitational field equations and work out the metric function that describe a black hole which generalizes the Maxwellian charged black hole of four-dimensional Einstein–Gauss–Bonnet gravity. Some basic thermodynamic quantities corresponding to the new black hole solution are computed and thermodynamic stability as well as thermal phase transitions are investigated.