Why the Universal Threshold for Primordial Black Hole Formation is Universal

TL;DR

This paper demonstrates that the threshold for primordial black hole formation remains consistent across different perturbation shapes when using the volume-averaged compaction function, due to the self-similar nature of gravitational collapse at criticality.

Contribution

It provides a theoretical proof explaining the universality of the primordial black hole formation threshold based on self-similarity and the compaction function.

Findings

Threshold is shape-independent when using the volume-averaged compaction function

Self-similarity of gravitational collapse explains the universality

Supports a unified criterion for primordial black hole formation

Abstract

We show why the threshold for primordial black hole formation is universal (independent from the shape of the perturbation) when expressed in terms of the volume averaged compaction function. The proof is rooted in the self-similarity of the gravitational collapse phenomenon at criticality.