Onset of chaotic gravitational lensing in non-Kerr rotating black holes with quadrupole mass moment

In the electromagnetic channel, chaotic gravitational lensing is a peculiar phenomenon in strong gravitational lensing. In this study, we analyze the properties and emergence of chaotic gravitational lensing in the Manko-Novikov black hole spacetime. Aiming to better understand the underlying physics, we elaborate on the boundaries of the accessible region through analyses of the contours of the effective potentials. The latter is associated with the two roots of a quadratic equation. In particular, we explore its interplay with an ergoregion, which leads to specific features of the effective potentials, such as the emergence of a cuspy edge and the formation of a pocket, which serve as static constraints on the geodesics. Additionally, we investigate the properties of the radial and angular accelerations at the turning points in photon trajectories. The accelerations are further examined and may provide kinematic constraints on the geodesics, as argued herein. It is concluded that the onset of the chaotic lensing is significantly related to both constraints; as a result, an arbitrary slight deviation in the incident photon is significantly amplified during evolution through an extensive period, demonstrating the complexity in the highly nonlinear deterministic gravitational system.