Collapse and dispersal of a homogeneous spin fluid in Einstein-Cartan theory

TL;DR

This paper demonstrates that incorporating spin effects of fermionic matter in Einstein-Cartan theory prevents gravitational collapse from forming singularities, leading instead to a bounce and re-expansion of the collapsing cloud.

Contribution

It introduces a model of gravitational collapse with spin effects using Weyssenhoff fluid, showing the avoidance of singularities and the occurrence of a bounce in Einstein-Cartan theory.

Findings

Collapse halts at finite radius due to spin effects.

No spacetime singularity forms; instead, a bounce occurs.

Horizon formation can be avoided below a certain mass threshold.

Abstract

In the present work, we revisit the process of gravitational collapse of a spherically symmetric homogeneous dust fluid which is known as the Oppenheimer-Snyder (OS) model [1]. We show that such a scenario would not end in a spacetime singularity when the spin degrees of freedom of fermionic particles within the collapsing cloud are taken into account. To this purpose, we take the matter content of the stellar object as a homogeneous Weyssenhoff fluid which is a generalization of perfect fluid in general relativity (GR) to include the spin of matter. Employing the homogeneous and isotropic FLRW metric for the interior spacetime setup, it is shown that the spin of matter, in the context of a negative pressure, acts against the pull of gravity and decelerates the dynamical evolution of the collapse in its later stages. Our results bode a picture of gravitational collapse in which the collapse process halts at a finite radius whose value depends on the initial configuration. We thus show that the spacetime singularity that occurs in the OS model is replaced by a non-singular bounce beyond which the collapsing cloud re-expands to infinity. Depending on the model parameters, one can find a minimum value for the boundary of the collapsing cloud or correspondingly a threshold value for the mass content below which the horizon formation can be avoided. Our results are supported by a thorough numerical analysis.