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

TL;DR

This study investigates the chaotic behavior of charged particles near magnetized black holes in Einstein-ModMax theory, using high-precision numerical methods and entropy-based indicators to distinguish regular and chaotic orbits.

Contribution

It introduces a symplectic integrator and applies Shannon entropy and mutual information to analyze chaos, providing new insights into particle dynamics in strong gravitational fields.

Findings

Indicators effectively distinguish between regular and chaotic orbits.

System parameters $e^{- u}$ and $Q_{m}$ have reduced sensitivity to orbital transitions.

Numerical solutions align with observational constraints from EHT.

Abstract

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.