Abstract
The equilibrium dynamics of the post-Newtonian circular restricted three-body problem (PNCRTBP), in the case of two massive stars or even stellar remnants, are investigated. Numerical methods are deployed for determining the points of equilibrium, as well as their linear stability. Our systematic and rigorous analysis reveals the role and influence of the transition parameter ∊ and the radiation pressure factor q on the dynamics of the system. It is revealed that the amount of equilibria increases with increasing value of the radiation pressure factor. On the other hand, as the value of the transition parameter tends to its maximum value the number of libration points is reduced, implying that in the case of strong post-Newtonian gravity the system degenerates.