Electromagnetic Fields of Separable Space-Times

TL;DR

This paper explores electromagnetic fields in Carter's separable space-times, revealing a rotation rate on spheroidal surfaces where electric and magnetic fields align, and finds that these systems share the Dirac electron's gyromagnetic ratio.

Contribution

It demonstrates the existence of a rotation rate on spheroidal surfaces in Carter's space-times where electromagnetic fields are aligned and shows these systems have the same gyromagnetic ratio as the Dirac electron.

Findings

Electric and magnetic fields are parallel and orthogonal to spheroids at a specific rotation rate.

All Carter separable systems without monopoles share the Dirac electron's gyromagnetic ratio.

Spheroidal surfaces act as equipotential surfaces in rotating axes.

Abstract

Carter derived the forms of the metric and the vector potentials of the space-times in which the relativistic Schrodinger equation for the motion of a charged particle separates. Here we show that on each `spheroidal' surface a rotation rate exists such that relative to those rotating axes the electric and magnetic fields are parallel and orthogonal to the spheroid which is thus an equipotential in those axes. All the finite Carter separable systems without magnetic monopoles or gravomagnetic NUT monopoles have the same gyromagnetic ratio as the Dirac electron.