Robinson-Trautman solution with scalar hair

TL;DR

This paper derives and analyzes a Robinson-Trautman solution with a scalar field, demonstrating the evolution of a naked singularity into a black hole horizon and examining its algebraic properties.

Contribution

The paper presents the first explicit Robinson-Trautman solution with a minimally coupled scalar field, including analysis of horizon formation and algebraic classification.

Findings

Curvature singularity initially naked, later enveloped by horizon

Solution is generally algebraic type II, reduces to D in spherical symmetry

Existence of quasilocal horizons proven using sub- and supersolution methods

Abstract

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.