Note on the absence of massive fermion superradiance from a Kerr black hole

Abstract

We point out the procedural fallacy in a recent proof by Martellini and Treves of the theorem that a massive fermion field in the Kerr metric does not super-radiate. The fallacy lies in arbitrarily switching from the spinor representation to Unruh's representation without any justification. This defect is remedied, and the correct proof of the theorem is exhibited. Further, an explicit demonstration generalizes the connection between this theorem and the positive definiteness of the norm shown by Unruh for the massless case.