Dynamic Cosmic Strings II: Numerical evolution of excited Cosmic Strings

TL;DR

This paper presents a stable, accurate numerical scheme for evolving cosmic strings coupled to gravity, analyzing their interaction with gravitational waves and their oscillatory behavior over time.

Contribution

It introduces a fully characteristic numerical method that includes null infinity, enabling precise boundary conditions and detailed analysis of cosmic string dynamics.

Findings

The numerical scheme is second order convergent and stable.

Cosmic strings oscillate at frequencies related to their scalar and vector field masses.

Strings exhibit ringing behavior after gravitational wave interaction, gradually returning to static states.

Abstract

An implicit, fully characteristic, numerical scheme for solving the field equations of a cosmic string coupled to gravity is described. The inclusion of null infinity as part of the numerical grid allows us to apply suitable boundary conditions on the metric and matter fields to suppress unphysical divergent solutions. The code is tested by comparing the results with exact solutions, checking that static cosmic string initial data remain constant when evolved and undertaking a time dependent convergence analysis of the code. It is shown that the code is accurate, stable and exhibits clear second order convergence. The code is used to analyse the interaction between a Weber--Wheeler pulse of gravitational radiation with the string. The interaction causes the string to oscillate at frequencies inversely proportional to the masses of the scalar and vector fields of the string. After the pulse has largely radiated away the string continues to ring but the oscillations slowly decay and eventually the variables return to their static values.