Chaos in the near-horizon dynamics of the dyonic $ m{AdS_4}$-Reissner-Nordström black hole

We investigate the chaos in the dynamics of a probe massless particle confined by the harmonic potential near the horizon of the dyonic $\rm{AdS_4}$-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 $λ_L$ 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 $λ_L$ 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.

💡 Research Summary

In this work the authors investigate chaotic dynamics of a mass‑less probe particle that is confined by an external harmonic potential in the near‑horizon region of a dyonic AdS₄ Reissner‑Nordström black brane. The black brane carries both electric charge (parameterised by the chemical potential µ) and magnetic charge (background magnetic field B). These two quantities enter the metric through the blackening factor

f(z)=1−(1+Γ)(z/z_h)³+Γ(z/z_h)⁴, Γ≡µ²z_h²+B²z_h⁴,

where z_h is the horizon radius and z=0 denotes the AdS boundary. The surface gravity κ=|f′(z_h)|/2 determines the Hawking temperature T=κ/2π; the extremal limit corresponds to Γ=3, for which κ→0 and T vanishes.

The particle’s Hamiltonian reads

E = p f(z)