The Onset of Chaotic Motion of a Spinning Particle around the Schwarzchild Black Hole

TL;DR

This paper demonstrates that the spin of a particle in Schwarzschild black hole spacetime can induce chaotic motion, with the Melnikov method revealing the entanglement of stable and unstable orbits as a trigger.

Contribution

It introduces the use of the Melnikov method to analyze how particle spin causes chaos in black hole environments, a novel application in this context.

Findings

Chaotic motion can be triggered by particle spin in Schwarzschild spacetime.

Stable and unstable orbits become entangled due to spin perturbations.

The Melnikov method effectively detects the onset of chaos.

Abstract

In the Schwarzchild black hole spacetime, we show that chaotic motion can be triggered by the spin of a particle. Taking the spin of the particle as a perturbation and using the Melnikov method, we find that the perturbed stable and unstable orbits are entangled with each other and that illustrates the onset of chaotic behavior in the motion of the particle.