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Analytical thresholds for black hole formation in general cosmological backgrounds

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arxiv 2007.05564 v2 pith:OE4KSPXA submitted 2020-07-10 gr-qc astro-ph.COhep-th

Analytical thresholds for black hole formation in general cosmological backgrounds

Albert Escriv\`a , Cristiano Germani , Ravi K. Sheth This is my paper
classification gr-qc astro-ph.COhep-th
keywords blackcompactioncosmologicaldeltaformationfunctionholeaccurate
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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 $p=w \rho$ with $w\in (0,1]$. Previous work has shown that when $w = 1/3$ (radiation), there is a critical threshold for black hole formation ($\delta_c$), 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 $w\gtrsim 1/3$; for smaller $w$s the knowledge of the full shape of the compaction function is necessary. We provide analytic approximations for $\delta_c$ which are accurate for $w\in [1/3,1]$.

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