Motion of charged particles near weakly magnetized Schwarzschild black hole

TL;DR

This paper investigates the motion of charged particles near a weakly magnetized Schwarzschild black hole, identifying different trajectory types and the critical magnetic field strength that causes a transition between them.

Contribution

It introduces a detailed analysis of bounded particle trajectories, including the critical magnetic field value and the gravitational drift effects, which are novel insights.

Findings

Existence of two trajectory types: curly and non-curly.

Critical magnetic field value for trajectory transition.

Gravitational drift influences the number of curls.

Abstract

We study motion of a charged particle in the vicinity of a weakly magnetized Schwarzschild black hole and focus on its bounded trajectories lying in the black hole equatorial plane. If the Lorentz force, acting on the particle, is directed outward from the black hole, there exist two qualitatively different types of trajectories, one is a curly motion and another one is a trajectory without curls. We calculated the critical value of the magnetic field for the transition between these two types. If the magnetic field is greater than the critical one, for fixed values of the particle energy and angular momentum, the bounded trajectory has curls. The curls appear as a result of the gravitational drift. The greater the value of the magnetic field, the larger is the number of curls. We constructed an approximate analytical solution for a bounded trajectory and found the gravitational drift velocity of its guiding center.