An interpretation of Robinson-Trautmann type N solutions

The Robinson-Trautmann type N solutions, which describe expanding gravitational waves, are investigated for all possible values of the cosmological constant A and the curvature parameter E. The wave surfaces are always (hemi-)spherical, with successive surfaces displaced in a way which depends on E. 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.