Chaos in the motion of a test scalar particle coupling to Einstein tensor in Schwarzschild-Melvin black hole spacetime

TL;DR

This paper investigates how coupling to Einstein tensor influences the chaotic motion of a scalar particle around Schwarzschild-Melvin black holes, revealing that coupling strength and sign significantly affect particle dynamics.

Contribution

It introduces the equation of motion for a scalar particle coupled to Einstein tensor in Schwarzschild-Melvin spacetime and analyzes the effects on chaos using multiple dynamical indicators.

Findings

Positive coupling can induce transitions between chaos and order.

Negative coupling tends to stabilize regular motion.

Coupling effects enrich the particle's dynamical behavior.

Abstract

We present firstly the equation of motion for a test scalar particle coupling to Einstein tensor in the Schwarzschild-Melvin black hole spacetime through the short-wave approximation. Through analysing Poincar\'{e} sections, the power spectrum, the fast Lyapunov exponent indicator and the bifurcation diagram, we investigate the effects of coupling parameter on the chaotic behavior of the particles. With the increase of the coupling strength, we find that the motion of coupled particle for the chosen parameters becomes more regular and order for the negative couple constant. While, for the positive one, the motion of coupled particles first undergoes a series of transitions between chaotic motion and regular motion and then falls into horizon or escapes to spatial infinite. Our results show that the coupling brings about richer effects for the motion of the particles.