Universal threshold for primordial black hole formation
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Abstract
In this letter, we argue and show numerically that the threshold to form\nprimordial black holes from an initial spherically symmetric perturbation is,\nto an excellent approximation, universal, whenever given in terms of the\ncompaction function averaged over a sphere of radius $r_m$, where $r_m$ is the\nscale on which the compaction function is maximum. This can be understood as\nthe requirement that, for a black hole to form, each shell of the averaged\ncompaction function should have an amplitude exceeding the so-called\nHarada-Yoo-Kohri limit. For a radiation dominated universe we argued, supported\nby the numerical simulations, that this limit is $\\delta_c = 0.40$, which is\nslightly below the one quoted in the literature. Additionally, we show that the\nprofile dependence of the threshold for the compaction function is only\nsensitive to its curvature at the maximum. We use these results to provide an\nanalytic formula for the threshold amplitude of the compaction function at its\nmaximum in terms of the normalised compaction function curvature at $r_m$.\n