Scalar and spinor perturbation to the Kerr–NUT spacetime

Abstract

We study the scalar and spinor perturbation, namely the Klein–Gordan and Dirac equations, in the Kerr–NUT spacetime. The metric is invariant under the duality transformation involving the exchange of mass and NUT parameters on the one hand and radial and angle coordinates on the other. We show that this invariance is also shared by the scalar and spinor perturbation equations. Further, by the duality transformation, one can go from the Kerr to the dual Kerr solution, and vice versa, and the same applies to the perturbation equations. In particular, it turns out that the potential barriers felt by the incoming scalar and spinor fields are higher for the dual Kerr than that for the Kerr. We also comment on the existence of horizon and singularity.