The onset of chaotic motion of a spinning particle around the Schwarzchild black hole

In the Schwarzschild 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