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

This article reviews the dynamics and observational signatures of particles interacting with monopoles, beginning with a scholium in Newton’sPrincipia. The orbits of particles in the field of a gravomagnetic monopole, the gravitational analog of a magnetic monopole, lie on cones; when the cones are slit open and flattened, the orbits are the ellipses and hyperbolas that one would have obtained without the gravomagnetic monopole. The more complex problem of a charged, spinning sphere in the field of a magnetic monopole is then discussed. The quantum-mechanical generalization of this latter problem is that of monopolar hydrogen. Previous work on monopolar hydrogen is reviewed and details of the predicted spectrum are given. Protons around uncharged monopoles have a bound continuum. Around charged ones, electrons have levels and decaying resonances, so magnetic monopoles can grow in mass by swallowing both electrons and protons. In general relativity, the spacetime produced by a gravomagnetic monopole is NUT space, named for Newman, Tamborino, and Unti (1963). This space has a nonspherical metric, even though a mass with a gravomagnetic monopole is spherically symmetric. All geodesics in NUT space lie on cones, and this result is used to discuss the gravitational lensing by bodies with gravomagnetic monopoles.