Relativistic Gravitational Collapse of a Cylindrical Shell of Dust II: Settling Down Boundary Condition

TL;DR

This paper investigates the gravitational collapse of a cylindrical dust shell, revealing that settling dust releases significant gravitational radiation and produces self-similar gravitational waves, contrasting with previous models that showed weak singularities.

Contribution

The study extends previous models by analyzing dust settling on the axis, demonstrating the emission of gravitational waves and self-similar behavior, unlike earlier collisionless particle models.

Findings

Infinite C-energy is released via gravitational radiation.

Gravitational waves exhibit self-similar asymptotic behavior.

Collapse leads to strong singularities with significant gravitational wave emission.

Abstract

We numerically study the dynamics of an imploding hollow cylinder composed of dust. Since there is no cylindrical black hole in 4-dimensional spacetime with physically reasonable energy conditions, a collapsed dust cylinder involves a naked singularity accompanied by its causal future, or a fatal singularity which terminates the history of the whole universe. In a previous paper, the present authors have shown that if the dust is assumed to be composed of collisionless particles such that these particles go through the symmetry axis of the cylinder, then the scalar polynomial singularity formed on the symmetry axis is so weak that almost all of geodesics are complete, and thus effectively no singularity forms by the collapse of a hollow dust cylinder. By contrast, in this paper, we assume that whole of the collapsed dust settles down on the symmetry axis by changing its equation of state. Obtained solutions are the straightforward extension of Morgan's null dust solution, in which no gravitational radiation is emitted. However, in the present case with timelike dust, infinite amount of $C$-energy initially stored in the system is released through gravitational radiation. We also show that the gravitational waves asymptotically behave in a self-similar manner.