Compatibility of nonlinear electrodynamics models with Robinson-Trautman geometry

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

Automated summary

The study investigates Robinson-Trautman solutions with nonlinear electrodynamics for both L(F) and L(F, G) Lagrangians, focusing on models representing regular black holes. The results demonstrate the clear uniqueness of Maxwell electrodynamics in terms of compatibility with the Robinson-Trautman class. Regular black hole models are not suitable for this class, and the famous Born-Infeld model highlights a key distinction between L(F) and L(F, G) in terms of the electric field obtained when the magnetic field is nontrivial.