Is there a mode stability paradox for neutrino perturbations of Kerr black holes?

TL;DR

This paper investigates the stability of Kerr black holes under neutrino perturbations, revealing a paradox where mode stability implies event horizon instability, challenging existing understanding of black hole physics.

Contribution

It derives a connection relation for massless Dirac fields on Kerr backgrounds, demonstrating a paradoxical link between mode stability and horizon instability.

Findings

Mode stability for neutrino perturbations is rigorously proven.

The same relation implies no superradiance for neutrinos.

A paradox links mode stability to event horizon instability.

Abstract

Adopting the notation of Teukolsky and Press, we derive the connection relation for asymptotic solutions of the massless Dirac equation on a Kerr background. We show that, unlike bosonic fields, the connection relation for massless Dirac fields (neutrino) provides a rigorous proof of mode stability. The same relation also implies that every incoming mode can be absorbed by the black hole or there is no superradiance. Recent works on overspinning black holes have shown that this can lead to the formation of naked singularities. We argue that the fact that both the mode stability of the black hole under neutrino perturbations and the instability of the event horizon (therefore the instability of the black hole) can be derived from the same connection relation leads to a paradox. In other words mode, stability implies event horizon instability as far as neutrino perturbations are concerned.