Instability and Information Production Around Kerr Black Holes: Effects on Entropy and the Shadow

Massless or massive particles in unstable orbits around a Kerr black hole exhibit exponentially unstable motion when perturbed. They either plunge into the black hole or escape to infinity after making some oscillations around the equatorial plane. This exponentially unstable motion causes information production. In the case of the photons that escape to infinity, it was recently suggested that this information can be used to resolve the subring structure of the shadow image and obtain more precise data about the black hole mass and spin. Here, we extend this method to obtain more precise results by including th non-equatorial contributions to the Lyapunov exponents. For massive particles plunging into the Kerr black hole, we show that the associated Kolmogorov-Sinai entropy derived from the Lyapunov exponents can be interpreted in the context of black hole thermodynamics and obeys Bekenstein's bound on the entropy of a physical system. Thus, the perturbed unstable orbits, either ending inside the black hole or at the observer's screen, have physical consequences.