Black hole formation from the gravitational collapse of a non-spherical network of structures

TL;DR

This paper investigates the gravitational collapse of non-spherical dust structures, finding that realistic black hole formation requires fine-tuned initial conditions, making such models unsuitable for astrophysical black holes but potentially relevant for primordial black holes.

Contribution

It demonstrates that non-spherical dust configurations cannot naturally form astrophysical black holes without unrealistic initial conditions, highlighting limitations of such models.

Findings

Realistic black hole formation from non-spherical dust requires fine-tuned initial conditions.

Non-spherical collapse leads to shell crossings, indicating stable virialized objects rather than black holes.

Constraints on mass and collapse time are incompatible with typical astrophysical black holes.

Abstract

We examine the gravitational collapse and black hole formation of multiple non--spherical configurations constructed from Szekeres dust models with positive spatial curvature that smoothly match to a Schwarzschild exterior. These configurations are made of an almost spherical central core region surrounded by a network of "pancake-like" overdensities and voids with spatial positions prescribed through standard initial conditions. We show that a full collapse into a focusing singularity, without shell crossings appearing before the formation of an apparent horizon, is not possible unless the full configuration becomes exactly or almost spherical. Seeking for black hole formation, we demand that shell crossings are covered by the apparent horizon. This requires very special fine-tuned initial conditions that impose very strong and unrealistic constraints on the total black hole mass and full collapse time. As a consequence, non-spherical non-rotating dust sources cannot furnish even minimally realistic toy models of black hole formation at astrophysical scales: demanding realistic collapse time scales yields huge unrealistic black hole masses, while simulations of typical astrophysical black hole masses collapse in unrealistically small times. We note, however, that the resulting time--mass constraint is compatible with early Universe models of primordial black hole formation, suitable in early dust-like environments. Finally, we argue that the shell crossings appearing when non-spherical dust structures collapse are an indicator that such structures do not form galactic mass black holes but virialise into stable stationary objects.