Applying explicit symplectic integrator to study chaos of charged particles around magnetized Kerr black hole

TL;DR

This paper applies a second-order explicit symplectic integrator to study the chaotic behavior of charged particles around magnetized Kerr black holes, revealing how magnetic and spacetime effects influence chaos.

Contribution

It demonstrates the effectiveness of a symplectic integrator in simulating nonintegrable charged particle dynamics in Kerr spacetime with magnetic fields, and explores chaos dependence on physical parameters.

Findings

Magnetic parameter increases chaos strength.

Spacetime dragging effects can weaken chaos.

No universal relation between black hole spin and chaos transition.

Abstract

In a recent work of Wu, Wang, Sun and Liu, a second-order explicit symplectic integrator was proposed for the integrable Kerr spacetime geometry. It is still suited for simulating the nonintegrable dynamics of charged particles moving around the Kerr black hole embedded in an external magnetic field. Its successful construction is due to the contribution of a time transformation. The algorithm exhibits a good long-term numerical performance in stable Hamiltonian errors and computational efficiency. As its application, the dynamics of order and chaos of charged particles is surveyed. In some circumstances, an increase of the dragging effects of the spacetime seems to weaken the extent of chaos from the global phase-space structure on Poincare sections. However, an increase of the magnetic parameter strengthens the chaotic properties. On the other hand, fast Lyapunov indicators show that there is no universal rule for the dependence of the transition between different dynamical regimes on the black hole spin. The dragging effects of the spacetime do not always weaken the extent of chaos from a local point of view.