Dynamics of Cosmic Strings in Schwarzschild Spacetime

TL;DR

This paper develops a numerical method to study the complex interaction between cosmic strings and Schwarzschild black holes, providing initial insights into their dynamics through simulations.

Contribution

It introduces a novel implicit finite difference scheme for simulating cosmic string dynamics in curved spacetime, validated against known solutions.

Findings

Numerical scheme accurately models cosmic string behavior near black holes

Preliminary results reveal possible string-black hole interaction patterns

Method enables future detailed studies of cosmic string dynamics

Abstract

Cosmic strings are topological defects thought to have formed early in the life of the universe. If such objects exist, a study of their interaction with black holes is of interest. The equations of motion of a cosmic string have the form of highly non-linear wave equations. General analytic solutions, except for motion in certain backgrounds such as flat and shockwave spacetimes, remain unknown; consequently, much of the work must be carried out numerically. To do this, an implicit finite difference scheme was developed that involves solving large block tridiagonal systems. This paper discusses the numerical method, its validation against analytic and semi-analytic solutions, and preliminary results on the interaction of a cosmic string with Schwarzschild black holes.