GLOBALLY STABLE EQUILIBRIA OF COLLISIONLESS SELF-GRAVITATING MATTER WITH NONVANISHING TOTAL ANGULAR-MOMENTUM

We demonstrate how to determine globally stable equilibrium states of collisionless self-gravitating matter with nonvanishing total angular momentum by a suitable energy minimization procedure. The distribution functions of the resulting equilibria depend on Jacoby's integral. In the minimization procedure we consider explicitly that the systems sh ould be gravitationally bound in all parts. With the help of a model r elaxation this technique can be used to determine final states of coll isionless relaxation. In our approach to that dissipationless (i.e., e nergy conserving) relaxation by mixing in phase space the final states are calculated as globally stable equilibria on macroscopic scales. T he energy conserving model relaxation increases entropy but does not m aximize entropy. This approach yields new aspects considering the depe ndence of the final states on the initial conditions.