On the dynamics of thin shells of counter-rotating particles

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 includes 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 two 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.