Dynamics of a string coupled to gravitational waves II - Perturbations propagate along an infinite Nambu-Goto string

TL;DR

This paper investigates the perturbative modes along a self-gravitating infinite string, revealing that string oscillations involve cosmic string traveling waves, using a gauge-invariant formalism within linearized Einstein equations.

Contribution

It extends previous analysis by including perturbation modes along the string and demonstrates the propagation of cosmic string traveling waves in the thin string limit.

Findings

Perturbative modes are identified along the string.

Oscillations involve cosmic string traveling waves.

Analysis is performed within a gauge-invariant formalism.

Abstract

The perturbative modes propagating along an infinite string are investigated within the framework of the gauge invariant perturbation formalism on a spacetime containing a self-gravitating straight string with a finite thickness. These modes are not included in our previous analysis. We reconstruct the perturbation formalism to discuss these modes and solve the linearized Einstein equation within the first order with respect to the string oscillation amplitude. In the thin string case, we show that the oscillations of an infinite string must involve the propagation of cosmic string traveling wave.