Classical Monopoles: Newton, NUT-space, gravomagnetic lensing and atomic spectra

TL;DR

This paper explores the classical and relativistic implications of gravomagnetic monopoles, revealing that all orbits in such fields lie on cones, and extends these concepts to atomic spectra and gravitational lensing.

Contribution

It uncovers the geometric nature of orbits around gravomagnetic monopoles and connects classical mechanics, atomic physics, and general relativity in this context.

Findings

All orbits in gravomagnetic monopole fields lie on cones.

The orbits become ellipses and hyperbolae when the cones are flattened.

Predicted spectrum of monopolar hydrogen matches known atomic physics principles.

Abstract

Stimulated by a scholium in Newton's Principia we find some beautiful results in classical mechanics which can be interpreted in terms of the orbits in the field of a mass endowed with a gravomagnetic monopole. All the orbits lie on cones! When the cones are slit open and flattened the orbits are exactly the ellipses and hyperbolae that one would have obtained without the gravomagnetic monopole. The beauty and simplicity of these results has led us to explore the similar problems in Atomic Physics when the nuclei have an added Dirac magnetic monopole. These problems have been explored by others and we sketch the derivations and give details of the predicted spectrum of monopolar hydrogen. Finally we return to gravomagnetic monopoles in general relativity. We explain why NUT space has a non-spherical metric although NUT space itself is the spherical space-time of a mass with a gravomagnetic monopole. We demonstrate that all geodesics in NUT space lie on cones and use this result to study the gravitational lensing by bodies with gravomagnetic monopoles. We remark that just as electromagnetism would have to be extended beyond Maxwell's equations to allow for magnetic monopoles and their currents so general relativity would have to be extended to allow torsion for general distributions of gravomagnetic monopoles and their currents. Of course if monopoles were never discovered then it would be a triumph for both Maxwellian Electromagnetism and General Relativity as they stand!