Electromagnetic waves in NUT space: Solutions to the Maxwell equations

TL;DR

This paper analytically solves Maxwell equations in NUT space using Newman-Penrose formalism, expressing solutions in terms of special functions and expanding in frequency perturbations.

Contribution

It provides the first analytical solutions to Maxwell equations in NUT space, utilizing separation of variables and special functions like Jacobi, Hypergeometric, and Heun's equations.

Findings

Angular solutions in terms of Jacobi polynomials

Radial solutions expressed via Hypergeometric and Heun's equations

Perturbative solutions expanded in frequency parameter

Abstract

In this paper, using the Newman-Penrose formalism, we find the Maxwell equations in NUT space and after separation into angular and radial components solve them analytically. All the angular equations are solved in terms of Jaccobi polynomials. The radial equations are transformed into Hypergeometric and Heun's equations with the right hand sides including terms of different order in the frequency of the perturbation which allow solutions in the expansion of this parameter.