Einstein-Cartan gravitational collapse of a homogeneous Weyssenhoff fluid

TL;DR

This paper investigates how torsion and spin effects in Einstein-Cartan gravity influence the gravitational collapse of a homogeneous Weyssenhoff fluid, revealing conditions for singularity formation, bounces, and horizon development.

Contribution

It provides new solutions for Einstein-Cartan collapse with spin effects, showing possible non-singular bounces and naked singularities in a homogeneous setting.

Findings

Collapse can result in singularities or bounces depending on spin parameters.

Certain conditions prevent trapped surface formation, leading to naked singularities.

There is an upper bound on the size of collapsing bodies for horizon formation.

Abstract

We consider the gravitational collapse of a spherically symmetric homogeneous matter distribution consisting of a Weyssenhoff fluid in the presence of a negative cosmological constant. Our aim is to investigate the effects of torsion and spin averaged terms on the final outcome of the collapse. For a specific interior spacetime setup, namely the homogeneous and isotropic FLRW metric, we obtain two classes of solutions to the field equations where depending on the relation between spin source parameters, $(i)$ the collapse procedure culminates in a spacetime singularity or $(ii)$ it is replaced by a non-singular bounce. We show that, under certain conditions, for a specific subset of the former solutions, the formation of trapped surfaces is prevented and thus the resulted singularity could be naked. The curvature singularity that forms could be gravitationally strong in the sense of Tipler. Our numerical analysis for the latter solutions shows that the collapsing dynamical process experiences four phases, so that two of which occur at the pre-bounce and the other two at post-bounce regimes. We further observe that there can be found a minimum radius for the apparent horizon curve, such that the main outcome of which is that there exists an upper bound for the size of the collapsing body, below which no horizon forms throughout the whole scenario.