Chaos in a Magnetized Modified Gravity Schwarzschild Spacetime

TL;DR

This paper investigates how chaos emerges in a magnetized modified gravity Schwarzschild spacetime, revealing that the modified gravity parameter enhances chaotic behavior of charged particles under certain conditions.

Contribution

It introduces explicit symplectic integrators for analyzing nonintegrable, magnetized modified gravity black hole spacetimes and demonstrates chaos dependence on various parameters.

Findings

Chaos increases with the modified gravity parameter.

Magnetic field strength and particle energy amplify chaos.

Higher particle angular momentum reduces chaos.

Abstract

Based on the scalar-tensor-vector modified gravitational theory, a modified gravity Schwarzschild black hole solution has been given in the existing literature. Such a black hole spacetime is obtained through the inclusion of a modified gravity coupling parameter, which corresponds to the modified gravitational constant and the black hole charge. In this sense, the modified gravity parameter acts as not only an enhanced gravitational effect but also a gravitational repulsive force contribution to a test particle moving around the black hole. Because the modified Schwarzschild spacetime is static spherical symmetric, it is integrable. However, the spherical symmetry and the integrability are destroyed when the black hole is immersed in an external asymptotic uniform magnetic field and the particle is charged. Although the magnetized modified Schwarzschild spacetime is nonintegrable and inseparable, it allows for the application of explicit symplectic integrators when its Hamiltonian is split into five explicitly integrable parts. Taking one of the proposed explicit symplectic integrators and the techniques of Poincare sections and fast Lyapunov indicators as numerical tools, we show that the charged particle can do chaotic motions under some circumstances. Chaos is strengthened with an increase of the modified gravity parameter from the global phase space structures. There are similar results when the magnetic field parameter and the particle energy increase. However, an increase of the particle angular momentum weakens the strength of chaos.