Dirac Equation on Kerr--Newman spacetime and Heun functions

TL;DR

This paper analyzes the Dirac equation in Kerr--Newman spacetime using a coordinate-free approach, reducing it to Heun-type equations, and recovers known results with a novel method.

Contribution

It introduces a pseudo-orthonormal coordinate-free method to separate the Dirac equation in Kerr--Newman spacetime and connects it to Heun functions, providing a new perspective.

Findings

Derivation of radial and angular equations in Kerr--Newman spacetime

Reduction to confluent Heun equations in the massless case

Reproduction of known results using a new approach

Abstract

By employing a pseudo-orthonormal coordinate-free approach, the Dirac equation for particles in the Kerr--Newman spacetime is separated into its radial and angular parts. In the massless case to which a special attention is given, the general Heun-type equations turn into their confluent form. We show how one recovers some results previously obtained in literature, by other means.