Scalar angular Teukolsky equation and its solution for the Taub-NUT spacetime
Phys. Rev. D 112, 124079 – Published 26 December, 2025
DOI: https://doi.org/10.1103/cfcz-kyqc
Abstract
The Taub-NUT spacetime offers many curious insights into the solutions of Einstein’s equation of general relativity. In the Bonnor interpretation, this spacetime possesses so-called Misner strings, which induce phenomena strikingly analogous to Dirac strings in the context of magnetic monopoles. The study of scattering in the latter case leads to a quantization of the product of electric charge and magnetic moment, sometimes called the Dirac condition. To enable a thorough discussion of scattering on the Taub-NUT spacetime, linear perturbations are considered in the Newman-Penrose formalism. From the resulting Teukolsky master equation angular and radial equations are derived by a separation ansatz. Here, our focus was limited to the scalar angular Teukolsky equation. We discussed it in detail, and derived the eigenvalues, subsequently solving the differential equation in terms of solutions to the confluent Heun equation. In the Bonnor interpretation of the Taub-NUT spacetime, there is no analog property to the Dirac condition. The choice of spacetime parameters remains unconstrained. However, in the Misner condition, one can rederive the well-known “Misner” condition, in which a product of frequency and NUT charge is of integer value. The results of this work will allow us to solve analytically for wave-optical scattering in order to, e.g., examine wave-optical images in the Taub-NUT spacetime.
