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

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 $λ$ 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 $e^{-itH}$.