Chaotic motion of charged test particles in a Kerr-MOG black hole with explicit symplectic algorithms
Zhenmeng Xu, Da‐Zhu Ma, Wenfu Cao, Kai Li
Abstract
Abstract The Kerr-MOG black hole has recently attracted significant research attention and has been extensively applied in various fields. To accurately characterize the long-term dynamical evolution of charged particles around a Kerr-MOG black hole, it is essential to utilize numerical algorithms that are high-precision, stable, and capable of preserving the inherent physical structural properties. In this study, we employ explicit symplectic algorithms combined with the Hamiltonian splitting technique to numerically solve the equations of motion for charged particles. Initially, by decomposing the Hamiltonian into five integrable components, three distinct explicit symplectic algorithms ( S 2, S 4, and $$PR{K_6}4)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>P</mml:mi> <mml:mi>R</mml:mi> <mml:msub> <mml:mi>K</mml:mi> <mml:mn>6</mml:mn> </mml:msub> <mml:mrow> <mml:mn>4</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> are constructed. Numerical experiments reveal that the $$PR{K_6}4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>P</mml:mi> <mml:mi>R</mml:mi> <mml:msub> <mml:mi>K</mml:mi> <mml:mn>6</mml:mn> </mml:msub> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> algorithm achieves superior accuracy. Subsequently, we utilize Poincaré sections and the fast Lyapunov indicator (FLI) to investigate the dynamic evolution of the particle. Our numerical results demonstrate that the energy E , angular momentum L , magnetic field parameter $$\beta ,$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>β</mml:mi> <mml:mo>,</mml:mo> </mml:mrow> </mml:math> black hole spin parameter a , and MOG parameter $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> all significantly influence the particle’s motion. Specifically, the chaotic region expands with an increase in E , $$\beta ,$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>β</mml:mi> <mml:mo>,</mml:mo> </mml:mrow> </mml:math> or $$\alpha ,$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>α</mml:mi> <mml:mo>,</mml:mo> </mml:mrow> </mml:math> but contracts with an increase in a or L . Furthermore, when any two of these five parameters are varied simultaneously, it becomes evident that a and L predominantly dictate the system’s behavior. This study not only offers novel insights into the chaotic dynamics associated with Kerr-MOG black holes but also extends the application of symplectic algorithms in strong gravitational fields.