On the equilibrium dynamics of a binary system with two Kerr-like bodies

Abstract

In this study, we investigate a system comprising of two Kerr-like bodies within the context of the planar circular restricted three-body problem. Our main objective is to explore how the equilibrium dynamics of the system are influenced by the free parameters present in the potential. To achieve this, we employ a combination of semi-analytical and numerical methods. Specifically, we numerically compute the coordinates, linear stability, and types of the libration points on the (x,y) plane. Additionally, we extend the analysis beyond a previously published paper by considering the general case where the main bodies of the system have different transition parameter values. In other words, the parameters that control the ratio between classical Newtonian and post-Newtonian gravity in each main body vary. Our findings reveal that this new setup, in contrast to the scenario with equal transition parameter values, exhibits a minimum of five equilibrium points, while the maximum number of equilibria remains unchanged at thirteen.