Construction of Explicit Symplectic Algorithm and Dynamical Research for String Motion in AdS5-Schwarzschild Black Hole
WANG Yingrong
XU Zhenmeng
MA Dazhu
Abstract：To address the issue that low-order non-symplectic algorithm easily induced pseudo chaos when simulating the dynamical evolution of strings near black hole event horizons,the construction of high-precision explicit symplectic algorithm was proposed,taking the five-dimensional anti-de Sitter-Schwarzschild(AdS5-Schwarzschild)black hole background as an example.The Hamiltonian of the system was decomposed into five integrable subparts,based on which two types of fourth-order explicit symplectic iterative schemes were designed.The successfully constructed explicit symplectic algorithm not only strictly preserved the symplectic structure of the system but also effectively suppressed the long-term truncation errors accumulated by low-order non-symplectic algorithm,significantly improving accuracy and computational efficiency.Leveraging the high-precision and long-term stable numerical solutions provided by the explicit symplectic algorithm,the analysis of Poincaré sections and Lyapunov exponent diagrams revealed that all stable orbits in the system exhibit ordered motion with no chaotic behavior.The numerical experiments aligned with theoretical analysis,demonstrating that the explicit symplectic algorithm accurately described the long-term dynamical evolution of strings in strong gravitational fields.This research provided a novel pathway for constructing explicit symplectic algorithms in strong gravitational astrophysical systems,holding significant practical implications.
Keywords：Symplectic algorithmstringAdS-Schwarzschild black holeHamiltonian systemchaotic dynamicsnumerical experiments
Publication Date：2025-12-30
Online Publishing Date：2025-12-10(First online date of this platform, not the publication date of the document)
Pages：6( 574-579 )