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 mu(min) necessary for the cosmic string loop to form a black hole according to the hoop conjecture is mu(min) = R/(2GL). Analyzing 25 576 loops, we obtain the empirical estimate f(BH) = 10(4.9 +/- 0.2)(G mu)(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 mu in the range 10(-3) less than or similar to G mu less than or similar to 3 x 10(-2). We use this power law to extrapolate to G mu similar to 10(-6), obtaining the fraction f(BH) 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 G mu less than or equal to 3.1(+/- 0.7) x 10(-6) on the cosmic string mass per unit length. This limit is consistent with all other observational bounds.