Robinson–Trautman solution with nonlinear electrodynamics

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.

Nonlinear electrodynamics AdS black hole and related phenomena in the extended thermodynamics

“…We note that other black hole solution for the model has also found in [100] via an alternative way. When α → 0, f (r ) goes back to the redshift function of RN-AdS black hole, f (r ) = 1 − r 2 3 − 2m 0 r + q 2 r 2 , as we expect.…”

Novel nonlinear electrodynamics black hole and related phenomena in the extended thermodynamics

“…We note that other black hole solution for the model has also found in [92] via an alternative way. When α → 0, f (r) goes back to the redshift function of RN-AdS black hole, f (r) = 1 − Λr 2 3 − 2m0 r + q 2 r 2 , as we expect.…”

Algebraic classification of Robinson-Trautman spacetimes

“…Moreover, new explicit solutions of this type in the Einstein gravity in D = 4 were found and studied, namely Robinson-Trautman solutions with minimally coupled free scalar field [11] and with electromagnetic field satisfying equations of nonlinear electrodynamics [12].…”