Motion of charged particles around a magnetic black hole/topological star with a compact extra dimension

TL;DR

This paper investigates the complex trajectories of charged particles around five-dimensional magnetic black holes or topological stars with a compact extra dimension, revealing rich dynamical structures and phase transition-like behavior.

Contribution

It introduces a detailed analysis of charged particle motion in five-dimensional solutions with a stabilized magnetic flux, uncovering novel phase transition phenomena in orbital dynamics.

Findings

Particle trajectories follow a Poincaré cone surface.

Existence of bound, plunging, or escaping orbits depends on constants of motion.

Swallow-tail structures in energy-angular momentum curves indicate phase transition-like behavior.

Abstract

We study the motion of charged particles in a family of five-dimensional solutions describing either a black hole or topological star with a fifth compact dimension stabilised by a magnetic flux. The particle's trajectory is shown to move along the surface of a Poincar\'{e} cone. The radial motion shows a rich structure where the existence of various bound, plunging, or escaping trajectories depend on the constants of motion. Curves of energy and angular momentum corresponding to spherical orbits show a swallow-tail structure highly reminiscent to phase transitions of thermodynamics. When the momentum along the compact direction is varied, the is a critical point beyond which the swallow-tail kink disappears and becomes a smooth curve.