Dynamical Evolution of a Cylindrical Shell with Rotational Pressure

TL;DR

This paper develops a framework to analyze cylindrical shell dynamics with rotational pressure, demonstrating that under certain conditions, collapsing shells bounce back and avoid singularities, with post-bounce behavior influenced by pressure signs.

Contribution

It provides a new analytical approach for cylindrical shell collapse with rotational pressure, showing shells bounce back under weak energy conditions and do not form singularities.

Findings

Shells bounce back if weak energy condition holds

Post-bounce behavior depends on pressure sign

Shells avoid reaching zero radius

Abstract

We prepare a general framework for analyzing the dynamics of a cylindrical shell in the spacetime with cylindrical symmetry. Based on the framework, we investigate a particular model of a cylindrical shell-collapse with rotational pressure, accompanying the radiation of gravitational waves and massless particles. The model has been introduced previously but has been awaiting for proper analysis. Here the analysis is put forward: It is proved that, as far as the weak energy condition is satisfied outside the shell, the collapsing shell bounces back at some point irrespective of the initial conditions, and escapes from the singularity formation. The behavior after the bounce depends on the sign of the shell pressure in the z-direction. When the pressure is non-negative, the shell continues to expand without re-contraction. On the other hand, when the pressure is negative (i.e. it has a tension), the behavior after the bounce can be more complicated depending on the details of the model. However, even in this case, the shell never reaches the zero-radius configuration.