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A disintegrating cosmic string

J. B. Griffiths, P. Docherty

TL;DR

The paper studies gravitational waves produced by a decaying cosmic string within the Robinson–Trautman type N vacuum solutions. It constructs a finite-duration 'sandwich' wave by patching Minkowski regions across a wave zone described by a holomorphic function $F(u,\zeta)$, resulting in a deficit angle that decays to zero over a finite retarded-time interval and leaves expanding Minkowski space behind. The main result is an explicit exact solution in which a cosmic string in front of the wave is gradually disintegrated, generating a spherical gravitational wave; in the limit $b\to 0$ with $ab$ finite, it reduces to the impulsive snapping-string solution, linking the sandwich construction to the known impulsive limit. The work clarifies how string dynamics can drive gravitational radiation in exact GR and sheds light on the singular structures inherent to Robinson–Trautman type N spacetimes.

Abstract

We present a simple sandwich gravitational wave of the Robinson-Trautman family. This is interpreted as representing a shock wave with a spherical wavefront which propagates into a Minkowski background minus a wedge. (i.e. the background contains a cosmic string.) The deficit angle (the tension) of the string decreases through the gravitational wave, which then ceases. This leaves an expanding spherical region of Minkowski space behind it. The decay of the cosmic string over a finite interval of retarded time may be considered to generate the gravitational wave.

A disintegrating cosmic string

TL;DR

The paper studies gravitational waves produced by a decaying cosmic string within the Robinson–Trautman type N vacuum solutions. It constructs a finite-duration 'sandwich' wave by patching Minkowski regions across a wave zone described by a holomorphic function , resulting in a deficit angle that decays to zero over a finite retarded-time interval and leaves expanding Minkowski space behind. The main result is an explicit exact solution in which a cosmic string in front of the wave is gradually disintegrated, generating a spherical gravitational wave; in the limit with finite, it reduces to the impulsive snapping-string solution, linking the sandwich construction to the known impulsive limit. The work clarifies how string dynamics can drive gravitational radiation in exact GR and sheds light on the singular structures inherent to Robinson–Trautman type N spacetimes.

Abstract

We present a simple sandwich gravitational wave of the Robinson-Trautman family. This is interpreted as representing a shock wave with a spherical wavefront which propagates into a Minkowski background minus a wedge. (i.e. the background contains a cosmic string.) The deficit angle (the tension) of the string decreases through the gravitational wave, which then ceases. This leaves an expanding spherical region of Minkowski space behind it. The decay of the cosmic string over a finite interval of retarded time may be considered to generate the gravitational wave.

Paper Structure

This paper contains 4 sections, 7 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The Robinson--Trautman type N solutions
  3. A sandwich Robinson--Trautman wave
  4. Conclusion

Figures (1)

  • Figure 1: The shaded region represents a sandwich gravitational wave at some time $t>0$. The expanding spherical wave surfaces are given by $u =$ const. The interior region behind the wave is Minkowski, while the outer region ahead of the wave is Minkowski minus a wedge representing a cosmic string.