Solutions to the Dirac Equation in Kerr-Newman Geometries including the black-hole region

TL;DR

This paper analyzes the Dirac equation in Kerr-Newman black hole geometries using advanced coordinate systems and formalisms, deriving asymptotic behaviors of solutions near critical regions.

Contribution

It introduces a method to separate the Dirac equation in Kerr-Newman spacetime and derives the asymptotic behavior of solutions at infinity and the Cauchy horizon.

Findings

Separation of the Dirac equation into radial and angular parts.

Asymptotic solutions at infinity and the Cauchy horizon.

Application of Newman-Penrose formalism in this context.

Abstract

We investigate the Dirac equation in Kerr-Newman space-time, using horizon penetrating coordinates (Eddington-Finkelstein-Coordinates) and the Newman-Penrose formalism to separate the equation into radial and angular systems of ordinary differential equations, and deriving the asymptotics of the radial solutions at infinity and at the Cauchy horizon.