Formation of black holes from collapsed cosmic string loops

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 μₘᵢₙ necessary for the cosmic string loop to form a black hole according to the hoop conjecture is μₘᵢₙ=R/(2GL). Analyzing 25 576 loops, we obtain the empirical estimate fBH=10^4.9±0.2(Gμ)^4.1±0.1 for the fraction of cosmic string loops which collapse to form black holes as a function of the mass per unit length μ in the range 10^-3Gμ3×10^-2. We use this power law to extrapolate to Gμ~10^-6, obtaining the fraction fBH of cosmologically interesting 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 Gμ<~3.1(±0.7)×10^-6 on the cosmic string mass per unit length. This limit is consistent with all other observational bounds.