Threshold of primordial black hole formation
Abstract
Based on a physical argument, we derive a new analytic formula for the amplitude of density perturbation at the threshold of primordial black hole formation in the Universe dominated by a perfect fluid with the equation of state p=wρc^{2} for w≥0. The formula gives δ_{Hc}^{UH}=sin^{2}[πw/(1+3w)] and δ∼_{c}=[3(1+w)/(5+3w)]sin^{2}[πw/(1+3w)], where δ_{Hc}^{UH} and δ∼_{c} are the amplitude of the density perturbation at the horizon crossing time in the uniform Hubble slice and the amplitude measure used in numerical simulations, respectively, while the conventional one gives δ_{Hc}^{UH}=w and δ∼_{c}=3w(1+w)/(5+3w). Our formula shows a much better agreement with the result of recent numerical simulations both qualitatively and quantitatively than the conventional formula. For a radiation fluid, our formula gives δ_{Hc}^{UH}=sin^{2}(3π/6)≃0.6203 and δ∼_{c}=(2/3)sin^{2}(3π/6)≃0.4135. We also discuss the maximum amplitude and the cosmological implications of the present result.
 Publication:

Physical Review D
 Pub Date:
 October 2013
 DOI:
 10.1103/PhysRevD.88.084051
 arXiv:
 arXiv:1309.4201
 Bibcode:
 2013PhRvD..88h4051H
 Keywords:

 04.70.Bw;
 97.60.Lf;
 95.35.+d;
 Classical black holes;
 Black holes;
 Dark matter;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Phenomenology;
 High Energy Physics  Theory
 EPrint:
 23 pages, 4 figures, minor correction, accepted for publication in Physical Review D, minor correction