Chaotic dynamics of charged particles near weakly magnetized black holes in Einstein-ModMax Theory

This paper presents a systematic study of the chaotic dynamics of charged test particles around purely magnetically charged black holes immersed in a uniform external magnetic field within the framework of Einstein-ModMax theory. By constructing an explicit symplectic integrator, we obtain high-precision numerical solutions of the equations of motion. Combining the observational constraints from the Event Horizon Telescope (EHT) shadow images, we further restrict the parameter ranges of the model. We apply Shannon entropy and MIPP (mutual information for particle pairs) as effective indicators to identify the chaotic behavior of charged test particles in the spacetime of this black hole. Numerical results indicate that these indicators can clearly distinguish between regular and chaotic motion of orbits in strong gravitational field systems. Further analysis reveals that, compared to the key conserved quantities that determine the global dynamical behavior of the system -- energy $E$ and angular momentum $L$, the sensitivity of the system parameters $e^{-\nu}$ and $Q_{m}$ to transitions in the orbital dynamical states is significantly reduced. This study provides a new perspective for a deeper understanding of the characterization and evolution mechanisms of chaotic dynamics in strong gravitational fields.