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Formation of black holes from collapsed cosmic string loops

Sep, 1995
20 pages
Published in:
  • Phys.Rev.D 53 (1996) 3002-3010
e-Print:
DOI:
Report number:
  • DAMTP-R-95-41,
  • WISC-MILW-95-TH-18
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Abstract: (arXiv)
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 LL which contracts to within a sphere of radius RR, the minimum mass-per-unit length μmin\mu_{\rm min} necessary for the cosmic string loop to form a black hole according to the hoop conjecture is μmin=R/(2GL)\mu_{\rm min} = R /(2 G L). Analyzing 25,57625,576 loops, we obtain the empirical estimate fBH=10 4.9±0.2(Gμ) 4.1±0.1f_{\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 μ\mu in the range 10 −3≲Gμ≲3×10 −210~{-3} \lesssim G\mu \lesssim 3 \times 10~{-2}. We use this power law to extrapolate to Gμ∼10 −6G\mu \sim 10~{-6}, obtaining the fraction fBHf_{\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 Gμ≤3.1(±0.7)×10 −6G\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.
  • 11.27.+d
  • 04.70.Bw
  • 98.70.Sa
  • 98.80.Cq
  • astrophysics: string
  • black hole: production
  • production: black hole
  • numerical calculations: interpretation of experiments