# Determination of chaotic behaviour in time series generated by charged particle motion around magnetized Schwarzschild black holes

## TL;DR

This paper investigates the chaotic behavior of charged particles in a magnetized Schwarzschild black hole environment, using various chaos detection methods including machine learning, to understand how magnetic and geometric parameters influence particle dynamics.

## Contribution

It introduces a comprehensive analysis of chaos in charged particle motion around black holes, employing machine learning techniques to identify chaotic regimes more efficiently.

## Key findings

- Chaotic behavior increases with the inclination angle.
- Machine learning outperforms traditional methods in detecting chaos.
- High inclination angles lead to more chaotic particle trajectories.

## Abstract

We study behaviour of ionized region of a Keplerian disk orbiting a Schwarzschild black hole immersed in an asymptotically uniform magnetic field. In dependence on the magnetic parameter ${\cal B}$, and inclination angle $\theta$ of the disk plane with respect to the magnetic field direction, the charged particles of the ionized disk can enter three regimes: a) regular oscillatory motion, b) destruction due to capture by the magnetized black hole, c) chaotic regime of the motion. In order to study transition between the regular and chaotic type of the charged particle motion, we generate time series of the solution of equations of motion under various conditions, and study them by non-linear (box counting, correlation dimension, Lyapunov exponent, recurrence analysis, machine learning) methods of chaos determination. We demonstrate that the machine learning method appears to be the most efficient in determining the chaotic region of the $\theta-r$ space. We show that the chaotic character of the ionized particle motion increases with the inclination angle. For the inclination angles $\theta \sim 0$ whole the ionized internal part of the Keplerian disk is captured by the black hole.