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We consider black holes which form from an initially spherically symmetric super-Hubble perturbation of a cosmological background filled by a perfect fluid p=w with w (0, 1]. Previous work has shown that when w = 1/3 (radiation), there is a critical threshold for black hole formation (c), which, to a very good approximation, only depends upon the curvature of the compaction function around its peak value. We find that this generalizes to all w 1/3; for smaller ws the knowledge of the full shape of the compaction function is necessary. We provide analytic approximations for c which are accurate for w 1/3, 1.
Escrivà et al. (Mon,) studied this question.
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