Gravitational Collapse of Cylindrical Shells Made of Counter-Rotating Dust Particles

TL;DR

This paper derives formulas for non-rotating cylindrical shells connecting different regions and studies how counter-rotating dust shells can either halt collapse or form line-like singularities, depending on angular momentum.

Contribution

It provides new general formulas for dynamic cylindrical shells and analyzes the effects of angular momentum on gravitational collapse outcomes.

Findings

Counter-rotating dust shells can prevent singularity formation when angular momentum is sufficient.

Collapse can be halted, avoiding singularities, due to angular momentum effects.

In some cases, a line-like singularity forms on the symmetry axis.

Abstract

The general formulas of a non-rotating dynamic thin shell that connects two arbitrary cylindrical regions are given using Israel's method. As an application of them, the dynamics of a thin shell made of counter-rotating dust particles, which emits both gravitational waves and massless particles when it is expanding or collapsing, is studied. It is found that when the models represent a collapsing shell, in some cases the angular momentum of the dust particles is strong enough to halt the collapse, so that a spacetime singularity is prevented from forming, while in other cases it is not, and a line-like spacetime singularity is finally formed on the symmetry axis.