On the periodic orbits in the Pseudo-Newtonian CR3BP with Kerr-like primaries

This research investigates the pseudo-Newtonian planar Circular Restricted three-body problem involving two Kerr-like primaries. We analyze the dynamics of a negligible third particle influenced by these two primary bodies rotating with identical angular velocities, while incorporating relativistic corrections to the gravitational field. The equations of motion are examined within a synodic coordinate framework, and the stable collinear libration points are identified. A Fourier series method is utilized to systematically develop periodic orbits around these points, employing an order-by-order decomposition of the series expansion. Both short and long periodic orbits are studied, and variational graphs are provided to demonstrate the relationship between the orbital period T and the mass ratio μ, as well as the Kerr perturbation factor ϵ, which account for non-Newtonian effects. Additionally, the research explores how these parameters affect the structure and evolution of periodic orbits, contributing valuable insights into the relativistic extension of classical CR3BP dynamics. Subsequently, by introducing the effective Kerr parameter ϵeff, we provided the first physical validation of this framework through its application to binary black hole merger events exemplified by GW190412, employing a gravitational-wave frequency–based approach that underscores the broader significance of our model.