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

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 Poincaré 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.

References added. Typos corrected. 24 pages, 10 figures

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• Motion of charged particles in spacetimes with magnetic fields of spherical and hyperbolic symmetry
• Quasinormal modes of a charged black hole with scalar hair
• Conformal scalar NUT-like dyons in conformal electrodynamics