Charged particle motions near non-Schwarzschild black holes with external magnetic fields in modified theories of gravity

TL;DR

This paper develops and applies explicit symplectic integrators to study charged particle dynamics near non-Schwarzschild black holes with magnetic fields in modified gravity theories, revealing how parameters influence chaos and stability.

Contribution

It introduces a new symplectic integration method suitable for non-Schwarzschild black hole spacetimes and investigates the effects of deformation parameters on particle orbit chaos.

Findings

Chaotic behavior increases with energy and magnetic field strength.

Positive deformation parameters tend to stabilize orbits.

The integrators perform well over long-term simulations.

Abstract

A small deformation controlled by four free parameters to the Schwarzschild metric could be referred to a nonspinning black hole solution in alternative theories of gravity. Because such a non-Schwarzschild metric can be changed into a Kerr-like black hole metric via a complex coordinate transformation, the recently proposed time-transformed explicit symplectic integrators for the Kerr type spacetimes are suitable for a Hamiltonian system describing the motion of charged particles around the non-Schwarzschild black hole surrounded with an external magnetic field. The obtained explicit symplectic methods are based on a time-transformed Hamiltonian split into seven parts, whose analytical solutions are explicit functions of new coordinate time. Numerical tests show that such explicit symplectic integrators for intermediate time-steps perform good long-term performance in stabilizing Hamiltonian errors regardless of regular or chaotic orbits. One of the explicit symplectic integrators with the techniques of Poincar\'{e} sections and fast Lyapunov indicators is applied to investigate the effects of the parameters including the four free deformation parameters on the orbital dynamical behavior. From the global phase-space structure, chaotic properties are typically strengthened under some circumstances as any one of the energy and the magnitudes of magnetic parameter and negative deformation parameters increases. However, they are weakened when each of the angular momentum and positive deformation parameters increases.