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

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 Poincaré 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.

Chaotic dynamics of strings around the Bardeen-AdS black hole surrounded by quintessence dark energy

“…In Fig. 2, we exhibit various forms of the effective potential (14). It is seen from the figure that the radii of the extreme points become smaller as the magnetic charge  increase and the particles can have orbits closer to the central black hole.…”

“…In general relativity, the geodesics of the common Schwarzschild [10,12], Reissner-Nordström [13], and Kerr [5,14] spacetime (as well as all axisymmetric and static black-hole geometries) are integrable, and there is no chaotic behavior in the geodesic motion of the particles [8]. Because the geodesic equations of particles are variably fractional and the dynamical system is accretive, researchers have concluded that geodesic motion is not the best way to detect chaos arising from black holes.…”