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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 $p=w\rho c^{2}$ for $w\ge 0$.
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B. J. Carr and T. Harada (unpublished)
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L. Alabidi, K. Kohri, M. Sasaki, and Y. Sendouda, J. Cosmol. Astropart. Phys. 05 ( 2013
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