Chaotic motion of Charged Particles in an Electromagnetic Field Surrounding a Rotating Black Hole

TL;DR

This paper investigates how the spin of a rotating black hole influences the chaotic motion of charged particles in its electromagnetic field, revealing that black hole spin can suppress chaos and induce regular trajectories.

Contribution

It provides a detailed analysis of charged particle trajectories near rotating black holes, highlighting the impact of black hole spin on chaotic dynamics and adiabatic invariants.

Findings

Black hole spin reduces chaotic motion of charged particles.

Spinning black holes can produce regular particle trajectories.

Dragging effects generate an approximate fourth adiabatic invariant.

Abstract

The observational data from some black hole candidates suggest the importance of electromagnetic fields in the vicinity of a black hole. Highly magnetized disk accretion may play an importance rule, and large scale magnetic field may be formed above the disk surface. Then, we expect that the nature of the black hole spacetime would be reveiled by magnetic phenomena near the black hole. We will start to investigate the motion of a charged particle which depends on the initial parameter setting in the black hole dipole magnetic field. Specially, we study the spin effects of a rotating black hole on the motion of the charged particle trapped in magnetic field lines. We make detailed analysis for the particle's trajectories by using the Poincar\'{e} map method, and show the chaotic properties that depend on the black hole spin. We find that the dragging effects of the spacetime by a rotating black hole weaken the chaotic properties and generate regular trajectories for some sets of initial parameters, while the chaotic properties dominate on the trajectories for slowly rotating black hole cases. The dragging effects can generate the fourth adiabatic invariant on the particle motion approximately.