Gravitational Radiation from Cylindrical Naked Singularity

TL;DR

This paper develops an approximate model to analyze gravitational radiation emitted from a cylindrical naked singularity formed by high-speed dust collapse, showing the emission can be gentle and the singularity's properties resemble null dust.

Contribution

It introduces a linear perturbation approach to approximate gravitational emission from a cylindrical naked singularity with specific boundary conditions ensuring finiteness.

Findings

Gravitational emission from the naked singularity can be gentle.

The singularity's properties are similar to those formed by null dust.

Boundary conditions ensure finiteness of variables at the singularity.

Abstract

We construct an approximate solution which describes the gravitational emission from a naked singularity formed by the gravitational collapse of a cylindrical thick shell composed of dust. The assumed situation is that the collapsing speed of the dust is very large. In this situation, the metric variables are obtained approximately by a kind of linear perturbation analysis in the background Morgan solution which describes the motion of cylindrical null dust. The most important problem in this study is what boundary conditions for metric and matter variables should be imposed at the naked singularity. We find a boundary condition that all the metric and matter variables are everywhere finite at least up to the first order approximation. This implies that the spacetime singularity formed by this high-speed dust collapse is very similar to that formed by the null dust and thus the gravitational emission from a naked singularity formed by the cylindrical dust collapse can be gentle.