Recurrence plots and chaotic motion around Kerr black hole

TL;DR

This paper investigates the dynamics of charged particles around a Kerr black hole in a magnetic field using recurrence plots, demonstrating their effectiveness in distinguishing regular and chaotic motion and identifying dynamical transitions.

Contribution

It introduces the use of recurrence plots and recurrence quantification analysis as novel tools for analyzing the dynamical regimes of particle motion near black holes.

Findings

Recurrence plots effectively visualize phase space recurrences.

RQA measures distinguish between regular and chaotic motion.

The method accurately detects transitions between dynamical regimes.

Abstract

We study the motion of charged test particles around a Kerr black hole immersed in the asymptotically uniform magnetic field, concluding that off-equatorial stable orbits are allowed in this system. Being interested in dynamical properties of these astrophysically relevant orbits we employ rather novel approach based on the analysis of recurrences of the system to the vicinity of its previous states. We use recurrence plots (RPs) as a tool to visualize recurrences of the trajectory in the phase space. Construction of RPs is simple and straightforward regardless of the dimension of the phase space, which is a major advantage of this approach when compared to the "traditional" methods of the numerical analysis of dynamical systems (for instance the visual survey of Poincar\'{e} surfaces of section, evaluation of the Lyapunov spectra etc.). We show that RPs and their quantitative measures (obtained from recurrence quantification analysis -- RQA) are powerful tools to detect dynamical regime of motion (regular vs. chaotic) and precisely locate the transitions between these regimes.