Regular and chaotic orbits near a massive magnetic dipole

TL;DR

This paper investigates the complex motion of neutral and charged particles near a massive magnetic dipole described by Bonnor's exact solution, revealing non-integrable dynamics and stable orbits influenced by gravitational and electromagnetic effects.

Contribution

It extends previous studies by analyzing particle dynamics in an exact Einstein-Maxwell solution, highlighting non-integrability and stable orbit regions in Bonnor spacetime.

Findings

Motion is non-integrable, exhibiting chaotic behavior.

Stable equatorial and levitating orbits exist depending on parameters.

Electromagnetic and gravitational effects are both significant in particle dynamics.

Abstract

Within the framework of Bonnor's exact solution describing a massive magnetic dipole, we study the motion of neutral and electrically charged test particles. In dependence on the Bonnor spacetime parameters, we determine regions enabling the existence of stable circular orbits confined to the equatorial plane and of those levitating above the equatorial plane. Constructing Poincar\'e surfaces of section and recurrence plots, we also investigate the dynamics of particles moving along general off-equatorial trajectories bound in effective potential wells forming around the stable circular orbits. We demonstrate that the motion in the Bonnor spacetime is not integrable. This extends previous investigations of generalized St\"ormer's problem into the realm of exact solutions of Einstein-Maxwell equations, where the gravitational and electromagnetic effects play a comparable role on the particle motion.