Chandrasekhar separation ansatz and the generalized total angular momentum for the Dirac equation in the Kerr-Newman metric

TL;DR

This paper establishes the eigenvalue relationship between the separation constant and a symmetry operator for the Dirac equation in Kerr-Newman spacetime, providing a complete solution framework and explicit propagator formula.

Contribution

It introduces the generalized total angular momentum operator J, proves its symmetry, and demonstrates the completeness of Chandrasekhar's separation ansatz for the Dirac equation in Kerr-Newman metric.

Findings

J is a symmetry operator for the Dirac equation in Kerr-Newman spacetime.

The separation constant λ is the eigenvalue of J.

An explicit formula for the propagator e^{-itH} is derived.

Abstract

In this paper we compute the square root of the generalized squared total angular momentum operator $J$ for a Dirac particle in the Kerr-Newman metric. The separation constant $\lambda$ arising from the Chandrasekahr separation ansatz turns out to be the eigenvalue of $J$. After proving that $J$ is a symmetry operator, we show the completeness of Chandrasekhar Ansatz for the Dirac equation in oblate spheroidal coordinates and derive an explicit formula for the propagator $e^{-itH}$.