An interpretation of Robinson-Trautman type N solutions

TL;DR

This paper analyzes Robinson-Trautman type N solutions describing expanding gravitational waves across different cosmological backgrounds, focusing on their geometric structure, explicit wave forms, and applications to cosmic strings.

Contribution

It provides a comprehensive investigation of these solutions for all cosmological constants and curvature parameters, including explicit examples and their global structures.

Findings

Wave surfaces are always (hemi-)spherical.

Explicit sandwich wave solutions are constructed in various backgrounds.

A family of solutions modeling snapping or decaying cosmic strings is analyzed.

Abstract

The Robinson-Trautman type N solutions, which describe expanding gravitational waves, are investigated for all possible values of the cosmological constant Lambda and the curvature parameter epsilon. The wave surfaces are always (hemi-)spherical, with successive surfaces displaced in a way which depends on epsilon. Explicit sandwich waves of this class are studied in Minkowski, de Sitter or anti-de Sitter backgrounds. A particular family of such solutions which can be used to represent snapping or decaying cosmic strings is considered in detail, and its singularity and global structure is presented.