Gravitational phase transition of fermionic matter in a general-relativistic framework

The Thomas–Fermi model at finite temperature is extended to describe a system of self-gravitating weakly interacting massive fermions in a general-relativistic framework. The existence and properties of the gravitational phase transition in this model are investigated numerically. It is shown that when a nondegenerate gas of weakly interacting massive fermions is cooled below some critical temperature, a condensed phase emerges, consisting of quasidegenerate fermion stars. For fermion masses of 10 to 25 keV, these fermion stars may very well provide an alternative explanation for the supermassive compact dark objects that are observed at galactic centers. Received: 23 April 1999 / Revised version: 24 June 1999 / Published online: 28 September 1999