High Speed Dynamics of Collapsing Cylindrical Dust Fluid

TL;DR

This paper develops an approximation method to analyze the final stages of cylindrical dust collapse, capturing gravitational wave generation as the dust approaches light speed near singularity formation.

Contribution

It introduces a high-speed approximation scheme that extends null dust solutions to describe realistic timelike dust collapse and gravitational wave emission.

Findings

Approximate solutions for late-stage cylindrical dust collapse.

Generation of gravitational waves during collapse.

Extension of null dust models to timelike dust scenarios.

Abstract

We construct approximate solutions that will describe the last stage of cylindrically symmetric gravitational collapse of dust fluid. Just before the spacetime singularity formation, the speed of the dust fluid might be almost equal to the speed of light by gravitational acceleration. Therefore the analytic solution describing the dynamics of cylindrical null dust might be the crudest approximate solution of the last stage of the gravitational collapse. In this paper, we regard this null dust solution as a background and perform `high-speed approximation' to know the gravitational collapse of ordinary timelike dust fluid; the `deviation of the timelike 4-velocity vector field from null' is treated as a perturbation. In contrast with the null dust approximation, our approximation scheme can describe the generation of gravitational waves in the course of the cylindrically symmetric dust collapse.