Dynamical Evolution of a Cylindrical Shell with Rotational Pressure

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.

To appear in Phys. Rev. D

References in corpus (1)

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

Cited by in corpus (4)

• Exact solutions for spherically gravitational collapse around a black hole: the effect of tangential pressure
• The effect of radiative gravitational modes on the dynamics of a cylindrical shell of counter rotating particles
• Relativistic dynamics of cylindrical shells of counter-rotating particles
• Analysis of Dynamic Axial-Symmetric Shells