Scalar and spinor perturbation to the most generalised Kerr-NUT space-time

TL;DR

This paper investigates scalar and spinor perturbations in the Kerr-NUT space-time, revealing duality symmetries and providing solutions that relate to known Kerr solutions, with implications for horizons and singularities.

Contribution

It demonstrates duality invariance of perturbation equations in Kerr-NUT space-time and derives solutions from known Kerr solutions under this symmetry.

Findings

Equations are invariant under duality transformations.

Solutions for Kerr-NUT can be obtained from Kerr solutions via duality.

Analysis of horizon and singularity conditions in Kerr-NUT space-time.

Abstract

We study the scalar and spinor perturbation to Kerr-NUT space-time, that is, Klein-Gordan and Dirac equation therein. The equations are invariant under duality transformation between the gravitational electric (M) and magnetic (l) charge, radial and angular coordinate, and radial and angular component of the field. We solve the equations separating into radial and angular parts. Moreover, if sets of Klein-Gordan and Dirac equation and corresponding solutions are known for Kerr space-time, under duality transformation, those in dual Kerr space-time are shown to be achieved. A few examples of solution are shown. We comment about the horizon and singularity conditions.