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

Arnold diffusion and geodesic dynamics of blackholes