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<p>We investigate the chaos in the dynamics of a probe massless particle confined by the harmonic potential near the horizon of the dyonic AdS<sub>4</sub>-Reissner-Nordström black hole. The total energy of the particle, chemical potential and magnetic field in this system serving as independently adjustable parameters tune nonlinearity and phase-space structure. By analyzing the trajectories on the Poincaré section and evaluating the Lyapunov exponents, we obtain the dynamical phase diagrams of the chaos and find their counteracting regulatory role: at low energy, chaos is enhanced and the Lyapunov exponent <i>λ</i><sub><i>L</i></sub> violates its upper bound (i.e. surface gravity) in the extremal black hole limit(combined paramete Γ = 3); at high energy, the same extremal limit suppresses chaos, with <i>λ</i><sub><i>L</i></sub> dropping to zero and a regular dynamical corridor emerging along Γ = 3 in the dynamical phase diagrams. These results establish a direct mapping between black hole thermodynamics and microscopic chaos, offering new insights into the AdS/QCD correspondence and nonlinear dynamics in strongly curved spacetimes.</p>

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Chaos in the near-horizon dynamics of the dyonic AdS4-Reissner-Nordström black hole

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  • 发表日期：

    2026年7月2日

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  • Mu-Yang Wang,
  • Si-Wen Li,
  • Defu Hou,
  • Dong Yan,
  • Yan-Qing Zhao

摘要

We investigate the chaos in the dynamics of a probe massless particle confined by the harmonic potential near the horizon of the dyonic AdS4-Reissner-Nordström black hole. The total energy of the particle, chemical potential and magnetic field in this system serving as independently adjustable parameters tune nonlinearity and phase-space structure. By analyzing the trajectories on the Poincaré section and evaluating the Lyapunov exponents, we obtain the dynamical phase diagrams of the chaos and find their counteracting regulatory role: at low energy, chaos is enhanced and the Lyapunov exponent λL violates its upper bound (i.e. surface gravity) in the extremal black hole limit(combined paramete Γ = 3); at high energy, the same extremal limit suppresses chaos, with λL dropping to zero and a regular dynamical corridor emerging along Γ = 3 in the dynamical phase diagrams. These results establish a direct mapping between black hole thermodynamics and microscopic chaos, offering new insights into the AdS/QCD correspondence and nonlinear dynamics in strongly curved spacetimes.