Motion of charged particles in an electromagnetic swirling universe: The complete set of solutions

TL;DR

This paper analytically solves the equations of motion for charged particles in an electromagnetic swirling universe, revealing new constants of motion and orbit types through elementary and elliptic functions.

Contribution

It provides the complete set of solutions for particle trajectories, including a new constant of motion, in a complex electromagnetic universe model.

Findings

Equations of motion can be decoupled and integrated analytically.

Existence of a fourth constant of motion.

Identification of various orbit types, including bounded and planar orbits.

Abstract

We discuss the motion of electrically and magnetically charged particles in the electromagnetic swirling universe. We show that the equations of motion can be decoupled in the Hamilton-Jacobi formalism, revealing the existence of a fourth constant of motion. The equations of motion can be analytically integrated. The solutions are presented in terms of elementary and elliptic functions. In addition, we discuss the possible orbits for both uncharged particles (in which case the motion is geodesic) and charged particles, respectively. A typical orbit is bounded in the radial direction and escapes to infinity in the $z-$ direction. However, the presence of the electromagnetic fields also leads to the existence of planar orbits.