  In this paper, we study the chaotic motion of a massive particle moving in a
perturbed Schwarzschild or Kerr background. We discover three novel orbits that
do not exist in the unperturbed cases. First, we find zoom-whirl orbits moving
around the photon shell which simultaneously exhibits Arnold diffusion: large
oscillations of particle's angular momentum and energy. Next, we show the
existence of oscillating orbits between a bounded region and infinity,
analogous to Newtonian three-body problem. Thirdly, we find that in perturbed
Kerr, there exists chaotic orbits around the event horizon that escapes the
event horizon after approaching it.
