The Dirac propagator in the Kerr-Newman metric

TL;DR

This paper provides an alternative proof of the completeness of the Chandrasekhar ansatz for the Dirac equation in Kerr-Newman spacetime, deriving integral representations for solutions and the propagator, including Minkowski space as a special case.

Contribution

It introduces a new proof of the Chandrasekhar ansatz's completeness and derives integral representations for the Dirac propagator in Kerr-Newman and Minkowski spacetimes.

Findings

Integral representation for solutions of the Dirac equation in Kerr-Newman

Explicit propagator for the Dirac equation in Minkowski space in oblate spheroidal coordinates

Confirmation of the completeness of the Chandrasekhar ansatz

Abstract

We give an alternative proof of the completeness of the Chandrasekhar ansatz for the Dirac equation in the Kerr-Newman metric. Based on this, we derive an integral representation for smooth compactly supported functions which in turn we use to derive an integral representation for the propagator of solutions of the Cauchy problem with initial data in the above class of functions. As a by-product, we also obtain the propagator for the Dirac equation in the Minkowski space-time in oblate spheroidal coordinates.