Fermionic microstates within the Painleve-Gullstrand black hole

We consider the quantum vacuum of a fermionic field in the presence of a black hole background as a possible candidate for the stabilized black hole. The stable vacuum state (as well as thermal equilibrium states at an arbitrary temperature) can exist if we use the Painleve-Gullstrand description of the black hole and the superluminal dispersion of the particle spectrum at high energy, which is introduced in the free-falling frame. This choice is inspired by the analogy between the quantum vacuum and the ground state of quantum liquid, in which the event horizon for the low-energy fermionic quasiparticles can also arise. The quantum vacuum is characterized by the Fermi surface that appears behind the event horizon. We do not consider the back reaction, and therefore, there is no guarantee that the stable black hole exists. But if it does exist, the Fermi surface behind the horizon would be the necessary attribute of its vacuum state. We also consider the exact discrete spectrum of fermions inside the horizon, which allows us to discuss the problem of fermion zero modes. (C) 2002 MAIK Nauka/Interperiodica.