Cosmic String Loops Collapsing to Black Holes

TL;DR

This paper analytically investigates the collapse probability of Turok's cosmic string loops into black holes, providing a refined calculation that clarifies previous discrepancies and enhances understanding of cosmic string evolution.

Contribution

It offers an exact analytical expression for collapse probability and a detailed classification of Turok strings, improving upon prior estimates with a significant numerical correction.

Findings

Collapse probability formula with a three-order magnitude correction

Classification of strings based on minimal size timing

Reconciliation of previous results for large Gμ values

Abstract

We examine the question of collapse of Turok's two-parameter family of cosmic strings. We first perform a classification of the strings according to the specific time(s) at which the minimal string size is reached during one period. We then obtain an exact analytical expression for the probability of collapse to black holes for the Turok strings. Our result has the same general behavior as previously obtained in the literature but we find, in addition, a numerical prefactor that changes the result by three orders of magnitude. Finally we show that our careful computation of the prefactor helps to understand the discrepancy between previously obtained results and, in particular, that for "large" values of $G\mu$, there may not even be a discrepancy. We also give a simple physical argument that can immediately rule out some of the previously obtained results.