On systems of self-gravitating bosons and fermions undergoing quantum condensation. Newtonian approach

Abstract

A system ofN self-gravitating bosons or fermions can, by loss of total energy, concentrate, gain gravitational energy, and heat up. If the particle numberN is smaller-than a critical numberNcritF ∼ (Planck mass/m)3 for fermions andNcritB ∼ (Planck mass/m)2 for bosons, the system canheat up to temperatures and concentrate to densities such that some particles will reach a quantum ground state, functional of the total particle number. By furthercooling of the system, theN particles approach well-known fully condensed or fully degenerate configurations. For bosons the appearance of a quantum condensed state leads to a phase transition of the first kind. ForN > NcritF fermions orN > NcritB bosons, the systems increase their temperature and condense to configurations for which a general relativistic treatment is mandatory. The concept of maximum temperature for a self-gravitating Bose and Fermi system is introduced.