On the dynamics of thin shells of counter rotating particles

TL;DR

This paper investigates the stability and dynamics of spherically symmetric thin shells composed of counter rotating particles, exploring conditions for stability, evaporation, and splitting into multiple shells, with explicit examples and a derivation of the thick to thin shell limit.

Contribution

It provides a comprehensive analysis of the stability conditions for shells with various velocity distributions and introduces criteria for shell splitting and evaporation, extending previous models.

Findings

Lower bound for shell compactness for stability

Conditions for single particle evaporation

Criteria for shell splitting into multiple shells

Abstract

In this paper we study the dynamics of self gravitating spherically symmetric thin shells of counter rotating particles. We consider all possible velocity distributions for the particles, and show that the equations of motion by themselves do not constrain this distribution. We therefore consider the dynamical stability of the resulting configurations under several possible processes. This include the stability of static configurations as a whole, where we find a lower bound for the compactness of the shells. We analyze also the stability of the single particle orbits, and find conditions for "single particle evaporation". Finally, in the case of a shell with particles whose angular momenta are restricted to two values, we consider the conditions for stability under splitting into two separate shells. This analysis leads to the conclusion that under certain conditions, that are given explicitly, an evolving shell may split into one or more separate shells. We provide explicit examples to illustrate this phenomenon. We also include a derivation of the thick to thin shell limit for an Einstein shell that shows that the limiting distribution of angular momenta is unique, covering continuously a finite range of values.