Arnold diffusion and geodesic dynamics of blackholes

TL;DR

This paper investigates chaotic geodesic motion of particles in perturbed black hole spacetimes, revealing novel orbits and Arnold diffusion phenomena that deepen understanding of black hole dynamics.

Contribution

It introduces three new types of orbits in perturbed Schwarzschild and Kerr backgrounds, including Arnold diffusion and horizon-escaping chaos, not seen in unperturbed cases.

Findings

Discovery of zoom-whirl orbits with Arnold diffusion

Existence of oscillating orbits between bounded regions and infinity

Chaotic orbits around the event horizon that can escape after approaching it

Abstract

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.