Chaos and fractals of the black hole photon ring

The photon ring of a Kerr black hole decomposes into a self-similar hierarchy of subrings. Here, we show that this self-similar structure persists in phase space. Moreover, near the photon shell of bound photon orbits, dynamics are controlled by a Lyapunov exponent γ, whose role we highlight by computing the first-return map for light rays close to an unstably bound orbit. Despite an exponential…