Chaotic motion of the charged test particle in a Kerr-MOG black hole with explicit symplectic algorithms

TL;DR

This paper develops and compares explicit symplectic algorithms for simulating charged particle dynamics around Kerr-MOG black holes, revealing how various parameters influence chaos and demonstrating the algorithms' high accuracy and stability.

Contribution

It introduces new symplectic algorithms tailored for Kerr-MOG black hole systems and analyzes their effectiveness in capturing complex chaotic behaviors.

Findings

The $PRK_6 4$ algorithm achieves the highest accuracy among tested methods.

Chaos increases with energy, magnetic field parameter, and MOG parameter.

Chaos decreases with black hole spin and angular momentum.

Abstract

The Kerr-MOG black hole has recently attracted significant research attention and has been extensively applied in various fields. To accurately characterize the long-term dynamical evolution of charged particles around Kerr-MOG black hole, it is essential to utilize numerical algorithms that are high-precision, stable, and capable of preserving the inherent physical structural properties. In this study, we employ explicit symplectic algorithms combined with the Hamiltonian splitting technique to numerically solve the equations of motion for charged particles. Initially, by decomposing the Hamiltonian into five integrable components, three distinct explicit symplectic algorithms ($S2$, $S4$, and $PR{K_6}4$) are constructed. Numerical experiments reveal that the $PR{K_6}4$ algorithm achieves superior accuracy. Subsequently, we utilize Poincar\'e sections and the Fast Lyapunov Indicator (FLI) to investigate the dynamic evolution of the particle. Our numerical results demonstrate that the energy $E$, angular momentum $L$, magnetic field parameter $\beta$, black hole spin parameter $a$, and MOG parameter $\alpha$ all significantly influence the particle's motion. Specifically, the chaotic region expands with increases in $E$, $\beta$, or $\alpha$, but contracts with increases in $a$ or $L$. Furthermore, when any two of these five parameters are varied simultaneously, it becomes evident that $a$ and $L$ predominantly dictate the system's behavior. This study not only offers novel insights into the chaotic dynamics associated with Kerr-MOG black holes but also extends the application of symplectic algorithms in strong gravitational field.