Analysis of Dynamic Axial-Symmetric Shells

TL;DR

This paper investigates the dynamical behavior of relativistic axial-symmetric shells, showing they remain at constant radius or collapse to zero, depending on conditions, challenging previous assumptions about their expansion or collapse.

Contribution

It demonstrates, using Israel's conservation equations, that such shells do not expand or collapse as previously thought, but stay at constant radius or collapse to zero, with implications for cylindrical flatness.

Findings

Shell remains at constant radius under certain conditions

Shell collapses to zero radius in null-collapse scenario

Imposing cylindrical flatness results in a boundary layer

Abstract

The aim of this work is to analyze the dynamical behavior of relativistic infinite axial-symmetric shells with flat interior and a radiation filled curved exterior spacetimes. It will be proven, by the use of conservation equations of Israel, that the given configuration does not let expansion or collapse of the shell which was proposed before, but rather the shell stays at constant radius. The case of null-collapse will also be considered in this work and it will be shown that the shell collapses to zero radius, and moreover, if cylindrical flatness is imposed a boundary layer is obtained still contrary to previous works.