Compatibility of nonlinear electrodynamics models with Robinson-Trautman geometry

Robinson-Trautman solutions with nonlinear electrodynamics are investigated for both $\mathbb{L}(F)$ and $\mathbb{L}(F,G)$ Lagrangians, the presence of electric magnetic charges as well electromagnetic radiation is assumed. Particular interest devoted to models representing regular black holes spherically symmetric situations. The results show clear uniqueness Maxwell respect compatibility class. Additionally, hole clearly not suited this class, while famous Born-Infeld model illustrates an important distinction between regards field we obtain when nontrivial.