Robinson--Trautman solution with nonlinear electrodynamics

TL;DR

This paper derives and analyzes explicit Robinson--Trautman solutions with nonlinear electromagnetic fields, showing singularity removal in electromagnetic fields but persistence of gravitational singularities, and exploring their algebraic types and asymptotic behavior.

Contribution

It introduces new Robinson--Trautman solutions with nonlinear electrodynamics, highlighting limitations in removing gravitational singularities beyond high-symmetry cases.

Findings

Electromagnetic singularities are removed in the solutions.

Gravitational singularities persist despite nonlinear electrodynamics.

Solutions are generally algebraic type II, reducing to type D in spherical symmetry.

Abstract

Explicit Robinson--Trautman solutions with electromagnetic field satisfying nonlinear field equations are derived and analyzed. The solutions are generated from the spherically symmetric ones. In all cases the electromagnetic field singularity is removed while the gravitational one persists. The models resolving curvature singularity were not possible to generalize to Robinson--Trautman geometry indicating that the removal of singularity in associated spherically symmetric case is just a consequence of high symmetry. We show that the solutions are generally of algebraic type II but reduce to type D in spherical symmetry. Asymptotically they tend to the spherically symmetric case as well.