Abstract
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 ρ with w ∊ (0,1]. Previous work has shown that when w = 1/3 (radiation), there is a critical threshold for black hole formation (δc), 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 δc which are accurate for w ∊ [1/3,1].