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arXiv · 2610.04521

Magnetic-field-induced chaos of charged particles around a rotating black hole in a King-type dark matter halo

Yu Wang·Meilin Liu·Haiguang Xu
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Abstract

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.

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Yu Wang, Meilin Liu, Haiguang Xu. 2026-10-12. Magnetic-field-induced chaos of charged particles around a rotating black hole in a King-type dark matter halo. https://arxiv.org/abs/2610.04521

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