Exact solutions to the Chandrasekhar Page angular equation

TL;DR

This paper derives exact, simple solutions for the Chandrasekhar Page angular equation, revealing eigenvalues that incorporate effects of black hole rotation and frame dragging, advancing understanding of Dirac particles in Kerr-Newman spacetime.

Contribution

It provides the first exact solutions to the Chandrasekhar Page angular equation, explicitly including the influence of black hole rotation and frame dragging effects.

Findings

Eigenvalues are the square root of total angular momentum plus a frame dragging term.

Solutions satisfy previously deduced asymptotic conditions.

Results confirm theoretical expectations about Dirac particles in rotating black hole spacetimes.

Abstract

Exact solutions are found for the Chandrasekhar Page angular equation which results when the Dirac equation in a Kerr Newman space time is separated into its radial and angular parts. The solutions turn out to be remarkably simple in form while satisfying the asymptotic conditions deduced earlier. The eigenvalues are found to be the square root of the total angular momentum as first found by Dirac for flat space; supplemented by a term which is the product of the mass of the Dirac particle times the specific angular momentum of the black hole. The additional contribution is what is expected from frame dragging.