Classical monopoles: Newton, NUT space, gravomagnetic lensing, and atomic spectra

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 1 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! 2

Matter without matter: Kaluza-Klein spacetime in Einstein-Gauss-Bonnet gravity

“…It may be asked how does the constraint equation permit presence of NUT parameter l which is interpreted as gravitational magnetic charge (see for example [27]). This happens because it is also the part of spacetime symmetry and there is no stress tensor T AB which generates NUT parameter.…”

Gravitomagnetism in the Kerr Newman Taub NUT spacetime

“…We employ this convention in the present work. Geodesic motion of test particles in the field of a gravitomagnetic monopole has been considered in [14,15] and in references cited there, while lensing aspects of a gravitomagnetic monopole have been discussed briefly in [15]. In the following section, we consider the effect of this monopole on the propagation of electromagnetic waves.…”

Nutty dyons

“…The first example of such a solution was found in 1963 by Newman, Unti and Tamburino (NUT) [6,7]. This metric has become renowned for being "a counterexample to almost anything" [8] and represents a generalization of the Schwarzschild vacuum solution [9] (see [10] for a simple derivation of this metric and historical review). It is usually interpreted as describing a gravitational dyon with both ordinary and magnetic mass 1 .…”