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

TL;DR

This paper presents an exact solution to Einstein's equations depicting a snapping cosmic string in a universe with a cosmological constant, generating impulsive gravitational waves and connecting to known wave families.

Contribution

It introduces a new exact solution modeling a snapping cosmic string in de Sitter or anti-de Sitter space, linking it to Robinson-Trautman waves and the C-metric.

Findings

Solution describes impulsive spherical gravitational waves from a snapping string

Connects the solution to Robinson-Trautman and C-metric families

Provides geometric interpretation and various metric forms

Abstract

We present and describe an exact solution of Einstein's equations which represents a snapping cosmic string in a vacuum background with a cosmological constant $\Lambda$. The snapping of the string generates an impulsive spherical gravitational wave which is a particular member of a known family of such waves. The global solution for all values of $\Lambda$ is presented in various metric forms and interpreted geometrically. It is shown to represent the limit of a family of sandwich type N Robinson-Trautman waves. It is also derived as a limit of the C-metric with $\Lambda$, in which the acceleration of the pair of black holes becomes unbounded while their masses are scaled to zero.