Cosmic String Loop Collapse in Full General Relativity

TL;DR

This paper presents the first full general relativistic simulations of cosmic string loops, analyzing their collapse behavior, gravitational wave emission, and implications for cosmic string production rates.

Contribution

It introduces fully relativistic simulations of cosmic string loops, predicting collapse outcomes and gravitational wave signals, advancing understanding beyond previous approximations.

Findings

Loops can unwind or form black holes depending on tension and size.

Gravitational wave emission during collapse is about 0.5% of loop mass.

A bound on cosmic string loop production rate is derived.

Abstract

We present the first fully general relativistic dynamical simulations of Abelian Higgs cosmic strings using 3+1D numerical relativity. Focusing on cosmic string loops, we show that they collapse due to their tension and can either (i) unwind and disperse or (ii) form a black hole, depending on their tension $G\mu$ and initial radius. We show that these results can be predicted using an approximate formula derived using the hoop conjecture, and argue that it is independent of field interactions. We extract the gravitational waveform produced in the black hole formation case and show that it is dominated by the $l=2$ and $m=0$ mode. We also compute the total gravitational wave energy emitted during such a collapse, being $0.5\pm 0.2~ \%$ of the initial total cosmic string loop mass, for a string tension of $G\mu=1.6\times 10^{-2}$ and radius $R=100~M_{pl}^{-1}$. We use our results to put a bound on the production rate of planar cosmic strings loops as $N \lesssim 10^{-2}~\mathrm{Gpc}^{-3}~\mathrm{yr}^{-1}$.