Robinson-Trautman solution with scalar hair

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.