Abstract
Explicit Robinson-Trautman solutions with an electromagnetic field satisfying nonlinear field equations are derived and analyzed. The solutions are generated from the spherically symmetric ones.
In all studied cases the electromagnetic field singularity is removed while the gravitational one persists. The models resolving the curvature singularity in spherically symmetric spacetimes could not be generalized to the Robinson-Trautman geometry using the generating method developed in this paper, which indicates that the removal of a singularity in the associated spherically symmetric case might be just a consequence of high symmetry.
We show that the obtained solutions are generally of algebraic type II and reduce to type D in spherical symmetry. Asymptotically they tend to the spherically symmetric case as well.