Dynamic Cosmic Strings I

TL;DR

This paper reformulates the equations for a time-dependent cosmic string coupled to gravity using Geroch decomposition, introduces a numerical method with conformal compactification, and explores interactions with gravitational radiation.

Contribution

It presents a new formulation of cosmic string dynamics in a reduced 2+1-dimensional framework and a numerical approach including null infinity for studying gravitational interactions.

Findings

Code reproduces vacuum solutions accurately

Method effectively handles asymptotically flat spacetimes

Prepares ground for analyzing cosmic string and gravitational wave interactions

Abstract

The field equations for a time dependent cylindrical cosmic string coupled to gravity are reformulated in terms of geometrical variables defined on a 2+1-dimensional spacetime by using the method of Geroch decomposition. Unlike the 4-dimensional spacetime the reduced case is asymptotically flat. A numerical method for solving the field equations which involves conformally compactifying the space and including null infinity as part of the grid is described. It is shown that the code reproduces the results of a number of vacuum solutions with one or two degrees of freedom. In the final section the interaction between the cosmic string and a pulse of gravitational radiation is briefly described. This will be fully analysed in the sequel.