Chaotic motion of scalar particle coupling to Chern-Simons invariant in Kerr black hole spacetime

TL;DR

This paper investigates the chaotic dynamics of a scalar particle coupled to the Chern-Simons invariant in Kerr black hole spacetime, revealing complex behaviors including chaos, transitions, and eventual escape or horizon capture.

Contribution

It introduces the equation of motion for the coupled scalar particle in Kerr spacetime and analyzes its chaotic behavior using various dynamical systems techniques.

Findings

Existence of chaos in scalar particle motion due to coupling

Transitions between chaotic and regular motion with increasing coupling

Particles eventually fall into the horizon or escape to infinity

Abstract

We present firstly the equation of motion for the test scalar particle coupling to the Chern-Simons invariant in Kerr black hole spacetime by the short-wave approximation. We have analyzed the dynamical behaviors of the test coupled particles by applying techniques including Poincar\'e sections, fast Lyapunov exponent indicator, bifurcation diagram and basins of attraction. It is shown that there exists chaotic phenomenon in the motion of scalar particle interacted with the Chern-Simons invariant in a Kerr black hole spacetime. With the increase of the coupling strength, the motion of the coupled particles for the chosen parameters first undergoes a series of transitions betweens chaotic motion and regular motion and then falls into horizon or escapes to spatial infinity. Thus, the coupling between scalar particle and Chern-Simons invariant yields the richer dynamical behavior of scalar particle in a Kerr black hole spacetime.