The self-gravitating Fermi gas

We discuss the nature of phase transitions in the self-gravitating Fermi gas at non-zero temperature. This study can be relevant for massive neutrinos in Dark Matter models and for collisionless self-gravitating systems experiencing a ``violent relaxation''. Below a critical energy (in the microcanonical ensemble) or below a critical temperature (in the canonical ensemble), the system undergoes a gravitational collapse leading to a compact object with a massive degenerate nucleus (fermion ball).