Scalar and Spinor Perturbation to the Kerr-NUT Spacetime

TL;DR

This paper investigates scalar and spinor perturbations in Kerr-NUT spacetime, revealing duality invariance in the equations and differences in potential barriers between Kerr and dual Kerr solutions.

Contribution

It demonstrates the invariance of perturbation equations under duality transformation and compares potential barriers in Kerr and dual Kerr spacetimes.

Findings

Perturbation equations are invariant under duality transformation.

Potential barriers are higher in dual Kerr than in Kerr.

Duality relates Kerr to dual Kerr solutions, affecting perturbation characteristics.

Abstract

We study the scalar and spinor perturbation, namely the Klein-Gordan and Dirac equations, in the Kerr-NUT space-time. The metric is invariant under the duality transformation involving the exchange of mass and NUT parameters on 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 existence of horizon and singularity.