Radiative spacetimes approaching the Vaidya metric

TL;DR

This paper studies a class of exact radiative solutions in general relativity that evolve from initial data to approach the Vaidya-(anti-)de Sitter spacetime, highlighting their existence, smoothness, and extensions.

Contribution

It demonstrates the existence and asymptotic approach of Robinson-Trautman solutions with pure radiation to the Vaidya-(anti-)de Sitter metric for smooth initial data.

Findings

Solutions exist for any sufficiently smooth initial data.

Spacetimes asymptotically approach the Vaidya-(anti-)de Sitter metric.

Extensions of the metric generally have finite smoothness.

Abstract

We analyze a class of exact type II solutions of the Robinson-Trautman family which contain pure radiation and (possibly) a cosmological constant. It is shown that these spacetimes exist for any sufficiently smooth initial data, and that they approach the spherically symmetric Vaidya-(anti-)de Sitter metric. We also investigate extensions of the metric, and we demonstrate that their order of smoothness is in general only finite. Some applications of the results are outlined.