Thermodynamic instability of self-gravitating heavy neutrino matter

It is shown, in the framework of the Thomas-Fermi model at finite temperature, that a cooling non-degenerate gas of massive neutrinos will, at a certain temperature, become unstable and undergo a first-order phase transition in which quasi-degenerate supermassive neutrino stars are formed through gravitational collapse. For neutrinos in the mass range of 10 to 25 keV/c$^{2}$, these compact dark objects could mimic the role of supermassive black holes that are reported to exist at the centres of galaxies and quasi-stellar objects.