An interpretation of Robinson Trautman type N solutions

Abstract

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

Robinson–Trautman solution with nonlinear electrodynamics

“…The general solution was given by Foster and Newman [21] and they are frequently used to form various sandwich-type waves [22]. There are no pure radiation solutions of type N.…”

A snapping cosmic string in a de Sitter or anti-de Sitter universe

“…In fact, it can be seen from figure 2 that the foliation of the space-time in either regions u < 0 or u > 0 by the null cones u = const. is only consistent with the parametrization of the Robinson-Trautman family of solutions with ǫ = 0 as described in [16]. In this parametrization, the solution (27) describes an impulsive spherical wave generated by the snapping of a cosmic string with deficit angle 2π(1−g) in a Minkowski, de Sitter or anti-de Sitter background according to the value of Λ.…”

“…(It can be seen from [16] that the most natural choice of parameter for these solutions is ǫ = 1. However, in the impulsive limit, all choices are permitted and the parameter ǫ is retained below.)…”

“…Although this produces a discontinuity in the metric function P and an impulsive component in (log P ) u , this construction may clearly be interpreted as the limit of a "well behaved" sandwich wave of the Robinson-Trautman family in which the metric is continuous. The geometrical structure of these solutions and the character of the singularities for different values of ǫ and Λ have been described in [16] for any g(u). Here, we apply this for an impulsive spherical wave generated by a snapping string in a de Sitter or anti-de Sitter background.…”

Type O pure radiation metrics with a cosmological constant

“…The analogous spacetimes with zero cosmological constant investigated in [13] revealed some complications and subtleties in the computer classification programmes [37], [18]; it will be interesting to see how the computer programmes handle these new spacetimes, and especially the existence of one degree of null isotropy. It will also be interesting to explore the physical interpretation of the spacetimes in this paper and in [11], along the lines investigated in [16] for the spaces with zero cosmological constant; the wide variety of individual subclasses with a range from zero to five Killing vectors give a rich area of investigation. In some classes of spacetimes the addition of a cosmological constant makes little significant difference.…”