Massless field perturbations and gravitomagnetism in the Kerr-Taub-NUT spacetime

TL;DR

This paper derives a unified master equation for spin $s extless=2$ perturbations in Kerr-Taub-NUT spacetime, analyzing their behavior and the effects of gravitomagnetic monopole and dipole moments on superradiance and harmonic solutions.

Contribution

It introduces a single gauge- and tetrad-invariant master equation for perturbations in Kerr-Taub-NUT spacetime, extending the analysis of superradiance and harmonic functions to include gravitomagnetic effects.

Findings

Radial functions' behavior at infinity and horizon analyzed.

Influence of gravitomagnetic monopole on superradiance studied.

Spin-weighted spheroidal harmonics generalized for Kerr-Taub-NUT.

Abstract

A single master equation is given describing spin $s\le2$ test fields that are gauge- and tetrad-invariant perturbations of the Kerr-Taub-NUT spacetime representing a source with mass $M$, gravitomagnetic monopole moment $-\ell$ and gravitomagnetic dipole moment (angular momentum) per unit mass $a$. This equation can be separated into its radial and angular parts. The behavior of the radial functions at infinity and near the horizon is studied and used to examine the influence of $\ell$ on the phenomenon of superradiance, while the angular equation leads to spin-weighted spheroidal harmonic solutions generalizing those of the Kerr spacetime. Finally the coupling between the spin of the perturbing field and the gravitomagnetic monopole moment is discussed.