Gravitational phase transitions in a one-dimensional spherical system

The behavior of gravitational phase transitions in a system of concentric, spherical, mass shells that interact via their mutual and self gravitation is investigated. The nature of the transition in the microcanonical, canonical, and grand canonical ensembles is studied both theoretically in terms of the mean field limit and by dynamical simulation. Transitions between a quasiuniform state and a centrally concentrated state are predicted by mean field theory for the microcanonical and canonical ensembles, and this is supported by dynamical simulation. For the grand canonical ensemble, mean field theory predicts that no transition takes place, and that the thermodynamically stable state is always the uniform one. Again, this is supported by simulations under various initial distributions of mass, even when the system is initialized in a collapsed state. In addition to testing the predictions of the mean field theory and studying the effects of finite size scaling, dynamical simulation allowed us to examine the behavior of temporal and positional correlations which are predicted to vanish in the mean field limit.