title: Statistical mechanics and thermodynamic limit of self-gravitating fermions in D dimensions.
abstract: 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> or =4, there exists a critical temperature (for sufficiently large systems) and a critical energy below which the system cannot be found in statistical equilibrium. Therefore, for D> or =4, quantum mechanics cannot stabilize matter against gravitational collapse. This is similar to a result found by Ehrenfest (1917) at the atomic level for Coulomb forces. This makes the dimension D=3 of our Universe very particular with possible implications regarding the anthropic principle. Our study joins a long tradition of scientific and philosophical papers that examined how the dimension of space affects the laws of physics.
authors.affiliation: Laboratoire de Physique Théorique, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse, France.
authors.forename: Pierre-Henri
authors.initials: PH
authors.lastname: Chavanis