Mean field theory of spherical gravitating systems

Important gaps remain in our understanding of the thermodynamics and statis tical physics of self-gravitating systems. Using mean field theory, here we investigate the equilibrium propel ties of several spherically symmetric m odel systems confined in a finite domain consisting of either point masses or rotating mass shells of different dimension. We establish a direct conne ction between the spherically symmetric equilibrium states of a self-gravit ating point mass system and a shell model of dimension 3. We construct the equilibrium density functions by maximizing the entropy subject to the usua l constraints of normalization and energy, but we also take into account th e constraint on the sum of the squares of the individual angular momenta, w hich is also an integral uf motion fur these symmetric systems. Two statist ical ensembles are introduced that incorporate the additional constraint. T hey are used to investigate the possible occurrence of a phase transition a s the defining parameters fur each ensemble are altered.