Interaction between a stationary electric charge and a stationary magnetic dipole

TL;DR

This paper explores the gravitational interactions between a stationary electric charge and magnetic dipole using Einstein-Maxwell theory, revealing the necessity of a torsion singularity to maintain their prescribed spins and the conditions under which it vanishes.

Contribution

It introduces the concept of a torsion singularity in the context of stationary electric and magnetic sources and analyzes the conditions for spin alignment.

Findings

Identification of a torsion singularity as a couple maintaining spins

The singularity vanishes under specific parameter conditions

Charge and magnet must spin relative to each other unless constrained

Abstract

Using Einstein-Maxwell theory I investigate the gravitational field generated by an electric charge and a magnetic dipole, both held in fixed positions, but spinning with prescribed angular momenta. There is a conical singularity between them representing a strut balancing the gravitational attraction of their masses. However, there is in general another singularity, which I call a torsion singularity. I interpret this as a couple needed to maintain the spins at their prescribed values. It vanishes when the parameters obey a certain formula. A conclusion of the work is that the charge and the magnet must spin relative to one another unless constrained by a couple.