On the beyond-Newtonian collinear circular restricted ( 3 + 1 ) $(3 + 1)$ -body problem with spinning primaries

In the present paper, a study on the beyond-Newtonian collinear circular restricted $(3+1)$ -body problem with spinning primaries is presented. In the setup of the collinear circular restricted four-body problem (CCR4BP), the three primaries are situated in the collinear central configuration where the masses of two peripheral primaries are equal. We have first derived the equations of motion for a system composed of three Kerr-like primaries. Further, we have unveiled how the existence, evolution, and stability of the libration points in the CCR4BP with beyond-Newtonian first-order correction terms and spin of the primaries depend on the mass parameter $\beta $ and control parameter $\varepsilon $ intending to manage the contribution of the beyond-Newtonian terms. It is observed that equilibria of the system are always even and varying from six to eighteen.