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

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.