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

TL;DR

This paper investigates chaotic dynamics of charged particles near GMGHS black holes using a new symplectic algorithm, revealing how electric and magnetic charges influence the transition between order and chaos.

Contribution

It introduces an optimized fourth-order symplectic algorithm for analyzing chaos in string-theoretic black holes and systematically studies the effects of electric and magnetic charges.

Findings

Chaos depends on electric charge and Coulomb parameter.

Order-to-chaos transition occurs with increasing electric charge.

Chaos emerges with increasing magnetic charge.

Abstract

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 necessitates high-precision numerical solutions, our prior research confirms the explicit symplectic algorithm as the optimal numerical integration tool for strongly curved gravitational celestial systems. Leveraging the Hamiltonian formulation of the GMGHS black hole, we develop an optimized fourth-order symplectic algorithm $PR{K_6}4$. This algorithm enables a systematic investigation of the chaotic motion employing four distinct chaos indicators: Shannon entropy, Poincare sections, the maximum Lyapunov exponents, and the Fast Lyapunov indicators. 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 arise with increasing $Q$ or decreasing $Q^*$. Conversely, in magnetically charged backgrounds, chaos emerges as $Q_m$ increases. These findings validate Shannon entropy as a robust chaos indicator within relativistic frameworks and provide novel insights on the dynamics of string-theoretic black holes.