Self-gravitating fluid shells and their non-spherical oscillations in Newtonian theory

TL;DR

This paper develops a formalism for analyzing surface flows in astrophysics and applies it to study non-spherical oscillations of self-gravitating fluid shells, revealing their stability properties under Newtonian gravity.

Contribution

It introduces a general formalism for surface flows and demonstrates the instability of self-gravitating spherical shells to non-radial perturbations in Newtonian theory.

Findings

Self-gravitating static shells are linearly unstable to non-radial perturbations.

Only shells with negative mass or balanced charge and tension are stable.

The formalism is suitable for various astrophysical applications.

Abstract

We summarize the general formalism describing surface flows in three-dimensional space in a form which is suitable for various astrophysical applications. We then apply the formalism to the analysis of non-radial perturbations of self-gravitating spherical fluid shells. Spherically symmetric gravitating shells (or bubbles) have been used in numerous model problems especially in general relativity and cosmology. A radially oscillating shell was recently suggested as a model for a variable cosmic object. Within Newtonian gravity we show that self-gravitating static fluid shells are unstable with respect to linear non-radial perturbations. Only shells (bubbles) with a negative mass (or with a charge the repulsion of which is compensated by a tension) are stable.