Formation of Black Holes from Collapsed Cosmic String Loops Typeset Using Revt E X 1

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 t 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 min necessary for the cosmic string loop to form a black hole according to the hoop conjecture is min = R=(2GL). Analyzing 25; 576 loops, we obtain the empirical estimate f BH = 10 4:90:2 (GG) 4:10:1 for the fraction of cosmic string loops which collapse to form black holes as a function of the mass-per-unit length in the range 10 3 < GG < 3 10 2. We use this power law to extrapolate to GG 10 6 , obtaining the fraction f 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 GG 3:1(0:7) 10 6 on the cosmic string mass-per-unit-length. This limit is consistent with all other observational bounds.