Black hole formation from the gravitational collapse of a nonspherical network of structures

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.

Gravitational entropy in Szekeres class I models

“…However, it is clear that Szekeres I models are still limited: by having a dust source (interpreted as CDM) and being Petrov type D, they belong to the class of 'silent' models in which local observers are unable to exchange information through wavelike effects (either acoustic waves through nonzero non-trivial pressure or gravitational waves by means of the magnetic Weyl tensor). Also, as commented before, the CET proposal only yields a unique effective energy tensor to derive gravitational entropy for spacetimes that are Petrov types D and N. There is still room for further evaluations since a Szekeres I model of multiple overdensities could collapse and form an apparent horizon as shown in [41]. This potentially represents a connection with the more familiar definitions of entropy of a black hole; an issue to be explored in the future.…”

Gravitational Entropy in Szekeres Class I Models

“…However, it is clear that Szekeres I models are still limited: by having a dust source (interpreted as CDM) and being Petrov type D, they belong to the class of "silent" models in which local observers are unable to exchange information through wavelike effects (either acoustic waves through nonzero nontrivial pressure or gravitational waves by means of the Magnetic Weyl tensor). Also, as commented before, the CET proposal only yields a unique effective energy tensor to derive gravitational entropy for spacetimes that are Petrov types D and N. There is still room for further evaluations since a Szekeres I model of multiple overdensities could collapse and form an apparent horizon as shown in [35]. This potentially represents a connection with the more familiar definitions of entropy of a black hole; an issue to be explored in the future.…”

Non-comoving baryons and cold dark matter in cosmic voids

“…Notice that as the evolution proceeds the density contrast at the surrounding wall increases, reaching probably a shellcrossing singularity. We interpret this as the onset of an intricate virialization process, a stage of structure formation that marks the limit of validity of the dust model, and that lies beyond the scope of this work (discussed elsewhere in the literature [83,84]). Since our purpose is to look at the simultaneous evolution of the matter-energy components (CDM and baryons) within the void before the onset of virialization, we have chosen z = 23 as the initial time slice, simply because it is easier to set the initial conditions at this time than at, say,…”