Motion of charged particles around a magnetized/electrified black hole

TL;DR

This paper analyzes the motion of charged particles around magnetized or electrically charged black holes using Ernst metrics, revealing stability conditions and complex trajectories like cycloids.

Contribution

It provides a detailed study of charged particle orbits in Ernst solutions with electric and magnetic fields, including stability analysis and explicit solutions for certain cases.

Findings

Electric field stability depends on a charge-specific critical value.

Charged particles exhibit cycloid-like trajectories in magnetic Ernst backgrounds.

Stable circular orbits exist only below certain electric field strengths.

Abstract

Geodesic equations of timelike and null charged particles in the Ernst metric are studied. We consider two distinct forms of the Ernst solution where the Maxwell potential represents either a uniform electric or magnetic field. Circular orbits in various configurations are considered, as well as their perturbations and stability. We find that the electric field strength must be below a certain charge-dependent critical value for these orbits to be stable. The case of the magnetic Ernst metric contains a limit which reduces to the Melvin magnetic universe. In this case the equations of motion are solved to reveal cycloidlike or trochoidlike motion, similar to those found by Frolov and Shoom around black holes immersed in test magnetic fields.