Relativistic dynamics of cylindrical shells of counter-rotating particles

TL;DR

This paper models the relativistic dynamics of cylindrical shells composed of counter-rotating particles, analyzing static solutions and gravitational wave emission using kinetic theory and junction conditions.

Contribution

It introduces an analytical kinetic theory model for cylindrical shells and explores their static and dynamic behaviors, including gravitational wave emission, through numerical and analytical methods.

Findings

Static solutions for single and double shells analyzed.

Numerical integration of equations of motion for dynamic shells.

Brief assessment of gravitational wave energy via Komar mass.

Abstract

Although infinite cylinders are not astrophysical entities, it is possible to learn a great deal about the basic qualitative features of generation of gravitational waves and the behavior of the matter conforming such shells in the limits of very small radius. We describe the analytical model using kinetic theory for the matter and the junction conditions through the shell to obtain its equation of motion. The nature of the static solutions are analyzed, both for a single shell as well as for two concentric shells. In this second case, for a time dependent external shell, we integrate numerically the equation of motion for several values of the constants of the system. Also, a brief description in terms of the Komar mass is given to account for the gravitational wave energy emitted by the system.