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

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.

Major changes, published version

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Cited by in corpus (11)

• Overspinning BTZ black holes with test particles and fields
• Can test fields destroy the event horizon in the Kerr-Taub-NUT spacetime?
• Kerr-Newman black holes can be generically overspun
• Over-spinning Kerr-Sen black holes with test fields
• String analog of Reissner-Nordström black holes cannot be overcharged
• Overspinning Kerr-MOG black holes by test fields and the third law of black hole dynamics
• Overcharging dilaton black holes in 2+1 dimensions to extremality and beyond
• Cosmic censorship, massless fermionic test fields, and absorption probabilities
• The variational method, backreactions, and the absorption probability in Wald type problems
• Spin-2 fields and cosmic censorship
• Second order variations and the overspinning problem in Kerr-Taub-NUT spacetime