Analysis of half-spin particle motion in Kerr-Newman field by means of effective potentials in second-order equations

TL;DR

This paper derives effective potentials for half-spin particles in Kerr-Newman fields, revealing singularities at horizons and proving no stationary bound states exist in extreme cases.

Contribution

It generalizes the method for obtaining effective potentials without separating variables and analyzes particle behavior in Kerr-Newman spacetime.

Findings

Effective potentials have singularities at horizons and specific parameters.

Stationary bound states do not exist in extreme Kerr-Newman fields.

The approach extends to non-separable variable cases.

Abstract

The self-conjugate Dirac Hamiltonian is obtained in the Kerr-Newman field. A transition is implemented to a Schr\"odinger-type relativistic equation. For the case where the angular and radial variables are not separated, the method of obtaining effective potentials is generalized. Effective potentials have isolated singularities on the event horizons as well as at certain parameters of the Kerr-Newman field and of the fermion in the neighborhoods of some values of the radial coordinate. For the extreme Kerr-Newman field, the impossibility of existence of stationary bound states of half-spin particles is proved.