Formation of Black Holes from Collapsed Cosmic String Loops

TL;DR

This paper estimates the fraction of cosmic string loops that form black holes, deriving a power law relation and setting an upper limit on the string tension based on observational constraints.

Contribution

It provides the first empirical estimate of black hole formation probability from cosmic string loops and derives a new upper bound on string tension.

Findings

Fraction of black hole-forming loops as a function of Gμ

Power law relation for collapse probability

Upper limit Gμ ≤ 3.1×10^{-6} from observational bounds

Abstract

The fraction of cosmic string loops which collapse to form black holes is estimated using a set of realistic loops generated by loop fragmentation. The smallest radius sphere into which each cosmic string loop may fit is obtained by monitoring the loop through one period of oscillation. For a loop with invariant length $L$ which contracts to within a sphere of radius $R$, the minimum mass-per-unit length $\mu_{\rm min}$ necessary for the cosmic string loop to form a black hole according to the hoop conjecture is $\mu_{\rm min} = R /(2 G L)$. Analyzing $25,576$ loops, we obtain the empirical estimate $f_{\rm BH} = 10^{4.9\pm 0.2} (G\mu)^{4.1 \pm 0.1}$ for the fraction of cosmic string loops which collapse to form black holes as a function of the mass-per-unit length $\mu$ in the range $10^{-3} \lesssim G\mu \lesssim 3 \times 10^{-2}$. We use this power law to extrapolate to $G\mu \sim 10^{-6}$, obtaining the fraction $f_{\rm BH}$ of physically interesting cosmic string loops which collapse to form black holes within one oscillation period of formation. Comparing this fraction with the observational bounds on a population of evaporating black holes, we obtain the limit $G\mu \le 3.1 (\pm 0.7) \times 10^{-6}$ on the cosmic string mass-per-unit-length. This limit is consistent with all other observational bounds.