Properties of Robinson--Trautman solution with scalar hair

Abstract

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.