Statistical mechanics and thermodynamic limit of self-gravitating fermions in D dimensions

Understand

We discuss the statistical mechanics of a system of self-gravitating fermions in a space of dimension $D$.

• We plot the caloric curves of the self-gravitating Fermi gas giving the temperature as a function of energy and investigate the nature of phase transitions as a function of the dimension of space.
• We consider stable states (global entropy maxima) as well as metastable states (local entropy maxima).
• We show that for $D\ge 4$, there exists a critical temperature (for sufficiently large systems) and a critical energy below which the system cannot be found in statistical equilibrium.