Hypocycloid motion in the Melvin magnetic universe

Abstract

The trajectory of a charged test particle in the Melvin magnetic universe is shown to take the form of hypocycloids in two different regimes, first of which is the class of perturbed circular orbits, and secondly in the weak-field approximation. In the latter case we find a simple relation between the charge of the particle and the number of cusps. These two regimes are within a continuously connected family of deformed hypocycloid-like orbits parametrised by the magnetic flux strength of the Melvin spacetime.

18 pages, 4 figures. Typos corrected. Introduction and conclusion improved thanks to the suggestions of the anonymous referee

References in corpus (8)

• Motion of charged particles near weakly magnetized Schwarzschild black hole
• Charging axisymmetric space-times with cosmological constant
• Bonnor-Melvin universe with a cosmological constant
• Motion of charged particles around a magnetized/electrified black hole
• Photon capture cones and embedding diagrams of the Ernst spacetime
• Mean eigenvalues for simple, simply connected, compact Lie groups
• Melvin universe as a limit of the C-metric
• Perihelion advance and trajectory of charged test particles in Reissner-Nordstrom field via the higher-order geodesic deviations