Chaos dynamics of charged particles near Gibbons-Maeda-Garfinkle-Horowitz-Strominger black holes

The Gibbons-Maeda-Garfinkle-Horowitz-Strominger (GMGHS) dilatonic black hole, a key solution in low-energy string theory, exhibits previously unexplored chaotic dynamics for charged test particles under electromagnetic influence. While characterizing such chaos requires high-precision numerical methods, our prior research identifies the explicit symplectic algorithm as the optimal integration tool for strongly curved gravitational systems. Leveraging the Hamiltonian formulation of the GMGHS black hole, we develop an optimized fourth-order symplectic algorithm, P R K 6 4 . This algorithm enables a systematic investigation of chaotic motion using four distinct chaos indicators: the Shannon entropy, Poincaré sections, the maximum Lyapunov exponent, and the Fast Lyapunov Indicator. Our results demonstrate a critical dependence of chaos on both electric charge ( Q , characterized by the Coulomb parameter Q * ) and magnetic charge ( Q m ). Specifically, in electrically charged backgrounds, order-to-chaos transitions occur with increasing Q . Conversely, in magnetically charged backgrounds, chaos emerges with increasing Q m . When Q and Q * vary simultaneously, the chaotic dynamics exhibit greater sensitivity to changes in Q * . Especially, these findings establish the Shannon entropy as a robust chaos indicator within relativistic frameworks and provide novel insights into the dynamics of string-theoretic black holes.