Abstract
A pseudo-Newtonian planar circular restricted three-body problem with two Kerr-like primaries is considered. Using numerical methods, we explore the dynamical properties of the points of equilibrium of the system. In particular, we demonstrate how the two main parameters of the system affect the properties (position and type) of the libration points. For all the equilibria, we present their nature by classifying them not only as linearly stable and unstable but also as maxima, index-1, and index-2 saddles. We also reveal the networks of simple symmetric periodic orbits and their linear stability.