The Antonov problem for rotating systems

We study the classical Antonov problem (of retrieving the statistical equilibrium properties of a self-gravitating gas of classical particles obeying Boltzmann statistics in space and confined in a spherical box) for a rotating system. It is shown that a critical angular momentum λ c (or, in the canonical language, a critical angular velocity ω c) exists, such that for λ < λ c the system's behaviour is qualitatively similar to that of a non-rotating gas, with a high energy disordered phase and a low energy collapsed phase ending with Antonov's limit, below which there is no equilibrium state. For λ > λ c , instead, the low-energy phase is characterized by the formation of two dense clusters (a " binary star "). Remarkably, no Antonov limit is found for λ > λ c. The thermodynamics of the system (phase diagram, caloric curves, local stability) is analyzed and compared with the recently-obtained picture emerging from a different type of statistics which forbids particle overlapping.