Fermionic microstates within Painlev\'e-Gullstrand black hole

TL;DR

This paper explores the quantum vacuum of fermionic fields in a black hole background using the Painlevé-Gullstrand description, proposing a stabilized black hole model with a Fermi surface behind the horizon, inspired by quantum liquids.

Contribution

It introduces a novel approach to black hole stabilization via fermionic vacuum states with superluminal dispersion in Painlevé-Gullstrand coordinates, highlighting the Fermi surface as a key feature.

Findings

Stable vacuum states exist with superluminal dispersion in this framework.

A Fermi surface appears behind the event horizon, characterizing the vacuum.

Exact fermion spectra allow analysis of fermion zero modes.

Abstract

We consider the quantum vacuum of 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 with arbitrary temperature) can exist if we use the Painlev\'e-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. Such 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 also can arise. The quantum vacuum is characterized by the Fermi surface, which appears behind the event horizon. We do not consider the back reaction, and thus 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 exact discrete spectrum of fermions inside the horizon which allows us to discuss the problem of fermion zero modes.