No abstract

In the presence of external, linear/nonlinear electromagnetic fields we integrate f (R) ∼ R + 2α √ R + const. gravity equations. In contrast to their Einsteinian cousins the obtained black holes are non-asymptotically flat with a deficit angle. In proper limits we obtain from our general solution the global monopole solution in f (R) gravity. The scale symmetry breaking term adopted as the nonlinear electromagnetic source adjusts the sign of the mass of the resulting black hole to be physical.

Explicit Robinson-Trautman solution with minimally coupled free scalar field is derived and analyzed. It is shown that this solution contains curvature singularity which is initially naked but later the horizon envelopes it. We use quasilocal horizon definition and prove its existence in later retarded times using sub-and supersolution method combined with growth estimates. We show that the solution is generally of algebraic type II but reduces to type D in spherical symmetry.

An explicit Robinson-Trautman solution with minimally coupled free scalar field was derived and analyzed recently. It was shown that this solution possesses a curvature singularity which is initially naked but later enveloped by a horizon. However, this study concentrated on the general branch of the solution where all free constants are nonzero. Interesting special cases arise when some of the parameters are set to zero. In most of these cases the scalar field is still present. One of the cases is a static solution which represents a parametric limit of the Janis-Newman-Winicour scalar field spacetime. Additionally, we provide a calculation of the Bondi mass which clarifies the interpretation of the general solution. Finally, by a complex rotation of a parameter describing the strength of the scalar field we obtain a dynamical wormhole solution.