发表机构
School of Physics and Astronomy, Shanghai Jiao Tong University; School of Aeronautics and Astronautics, Shanghai Jiao Tong University（上海交通大学物理与天文学院; 上海交通大学航空航天学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究King型暗物质晕中旋转黑洞周围带电粒子在磁场下的动力学，发现磁耦合增强可引发混沌，且晕密度与初始条件影响轨道稳定性。
AI 中文摘要
我们研究了嵌入King型暗物质晕中的旋转黑洞周围带电测试粒子的动力学，该系统受到一个预先给定的、渐近均匀的磁场作用。我们采用由静态晕种子通过修正的Newman--Janis方案构造的有效旋转几何，以及一个在非真空背景中通常需要支撑电流的测试电磁场。在没有磁耦合的情况下，类时Hamilton--Jacobi方程可分离变量，并允许一个Carter型常数，从而提供一个可积的参考系统。我们使用庞加莱截面和切向量增长诊断来刻画轨道动力学，包括快速Lyapunov指标和有限时间Lyapunov指数，并进行质量壳监测和数值细化检查。对于采样的初始条件，增加磁耦合可以产生从规则运动到具有持续正有限时间增长率的散乱庞加莱截面的转变。在固定磁耦合下，两个较高密度晕的情况对代表性混沌轨道族产生较大的有限时间指数，而弱晕修正未能在数值细化下得到一致分辨。一个不同的初始条件产生闭合的庞加莱曲线，并在扩展积分期间递减的有限时间指数，支持尽管存在非零磁耦合仍为规则运动。这些结果表明，King型晕以依赖于初始条件的方式调制磁场诱导的轨道不稳定性，而规则运动在磁化系统中持续存在。
英文摘要
We investigate the dynamics of charged test particles around a rotating black hole embedded in a King-type dark matter halo and subjected to a prescribed, asymptotically uniform magnetic field. We adopt an effective rotating geometry constructed from a static halo seed through a modified Newman--Janis prescription and a test electromagnetic field that generally requires supporting currents in the nonvacuum background. In the absence of magnetic coupling, the timelike Hamilton--Jacobi equation separates and admits a Carter-type constant, providing an integrable reference system. We characterize the orbital dynamics using Poincaré sections and tangent-vector growth diagnostics, including fast Lyapunov indicators and finite-time Lyapunov exponents, with mass-shell monitoring and numerical refinement checks. For the sampled initial conditions, increasing the magnetic coupling can produce a transition from regular motion to scattered Poincaré sections with sustained positive finite-time growth rates. At fixed magnetic coupling, the two higher-density halo cases yield larger finite-time exponents for a representative chaotic orbit family, whereas the weak-halo correction is not resolved consistently under numerical refinement. A different initial condition yields a closed Poincaré curve and a decreasing finite-time exponent over an extended integration, supporting regular motion despite the nonzero magnetic coupling. These results show that the King-type halo modulates magnetic-field-induced orbital instability in an initial-condition-dependent manner, while regular motion persists within the magnetized system.
Comments18 pages, 7 figures
