Properties of Robinson--Trautman solution with scalar hair

TL;DR

This paper explores various special cases of a Robinson--Trautman solution with scalar hair, revealing static, wormhole, and other configurations, and clarifies their properties through mass calculations and parameter analysis.

Contribution

It provides a detailed analysis of special cases of the Robinson--Trautman solution with scalar hair, including static and wormhole solutions, and offers insights into their physical properties.

Findings

Existence of static scalar field solutions as limits of the general case.

Identification of a dynamical wormhole solution via parameter rotation.

Calculation of Bondi mass clarifies the physical interpretation.

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.