Charged Particle Dynamics and Chaos-Bound Violation in Rotating Einstein–Euler–Heisenberg Black Hole Spacetimes

The motion and Lyapunov instability of charged particles around a rotating Einstein–Euler–Heisenberg black hole (EEHBH) is explored systematically, and the chaos-bound, [Formula: see text], is discussed in the light of that. The equilibrium positions and their stability are examined for various values of the angular momenta and the charge-to-mass ratios of the particles. We find that there exist certain values of the electric charge, rotation, and Euler–Heisenberg coupling for which the chaos bound is broken, even at relatively low angular momentum. For [Formula: see text], the Euler–Heisenberg coupling has little effect on the horizon radius; but, for larger charge values, its impact becomes noticeable. On the other hand, it greatly alters the surface gravity, especially when rotation and charge are present. The extremal case shows a larger chaos bound violation, while the non-extremal case shows a more complex angular momentum dependence. This work presents a comprehensive analysis of the effects of both the rotational and frame-dragging and/or nonlinear electrodynamics on the equilibrium structure, Lyapunov instability, and stability/chaos transitions associated with charged-particle motion, unlike previous studies which examined these combined effects separately.