Regular and Chaotic Motion in General Relativity: The Case of a Massive Magnetic Dipole

TL;DR

This paper explores the equilibrium and chaotic dynamics of charged particles around a massive magnetic dipole in general relativity, using exact solutions and chaos detection techniques.

Contribution

It introduces an analysis of particle motion near a massive magnetic dipole, highlighting conditions for stability and chaos within a relativistic framework.

Findings

Identification of stable regions of particle motion.

Detection of chaotic behavior in particle trajectories.

Application of Poincaré sections and recurrence plots for chaos analysis.

Abstract

Circular motion of particles, dust grains and fluids in the vicinity of compact objects has been investigated as a model for accretion of gaseous and dusty environment. Here we further discuss, within the framework of general relativity, figures of equilibrium of matter under the influence of combined gravitational and large-scale magnetic fields, assuming that the accreted material acquires a small electric charge due to interplay of plasma processes and photoionization. In particular, we employ an exact solution describing the massive magnetic dipole and we identify the regions of stable motion. We also investigate situations when the particle dynamics exhibits the onset of chaos. In order to characterize the measure of chaoticness we employ techniques of Poincar\'e surfaces of section and of recurrence plots.