标题： 带电测试粒子在Kerr-MOG黑洞中的混沌运动及显式辛算法 显示英文标题

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

摘要： 最近，Kerr-MOG 黑洞引起了广泛的研究兴趣，并已被广泛应用于星系旋转曲线、星系团中的引力透镜效应以及宇宙中大尺度结构的形成等领域。 在本文中，我们主要关注带电粒子在 Kerr-MOG 黑洞周围的动力学行为。 首先，给出了在标量-张量-矢量引力（STVG）理论下带电粒子的场方程。 然后，根据哈密顿系统的特性，哈密顿可以分解为五个可积部分，并构建了三种显式辛算法。 数值实验表明，算法（$PR{K_6}4$）是最优的。 最后，使用庞加莱截面和快速李雅普诺夫指标（FLI）来探索粒子的动力学演化。 从数值结果中很容易发现，能量$E$，角动量$L$，磁场参数$\beta$，黑洞自转参数$a$，以及引力场强度参数$\alpha$对粒子的运动有影响。 特别是，当$E$、$\beta$或$\alpha$增加时，混沌区域会增加，但随着$a$或$L$的增加，混沌区域会减少。 此外，当同时应用五个参数中的任意两个时，很容易观察到$a$和$L$起主导作用。 显示英文摘要

摘要： Recently, Kerr-MOG black hole has attracted widespread research interest and has been widely used in fields such as galaxy rotation curves, gravitational lensing in galaxy clusters, and the formation of large-scale structures in the universe. In this paper, we mainly focus on dynamics of the charged particle around Kerr-MOG black hole. At first, the field equations for the charged particle under the Scalar-Tensor-Vector Gravity (STVG) theory are presented. Then, according to the characteristics of the Hamiltonian system, the Hamiltonian can be decomposed into five integrable parts, and three kinds of explicit symplectic algorithms are constructed. Numerical experiments show that the algorithm ($PR{K_6}4$) is the optimal one. At last, the Poincar\'e section and the fast Lyapunov indicator (FLI) are used to explore dynamic evolution of the particle. From the numerical results, it is easy to find that the energy $E$, the angular momentum $L$, the magnetic field parameter $\beta$, the black hole spin parameter $a$, and the gravitational field strength parameter $\alpha$ have an impact on the motion of the particle. In particular, the chaotic region increases as $E$, $\beta$, or $\alpha$ increases, but decreases with the increases of $a$ or $L$. Moreover, when any two of the five parameters are applied simultaneously, it is easy to observe that $a$ and $L$ play a dominant role.