Pulsating binary pulsars- with a new class of stars in a restricted 4-body problem

A pulsating binary pulsar are examined in the Restricted Three-Body Problem. For comparable primary weights that travel in symmetric-like trajectories, the barycenter is the center of rotation acting as a common foci for the two free trajectories. The normalization constant value l in the equations of motion is now a function of time. A phase-space integral equation solution identifies the L1 Libration point as a stationary point with no centrifugal or gravitational forces where rotational rate is an eigenvalue. If space debris exists at Libration Points other than L1, stray mass would potentially leave the system. Thus, this discovery may lead to a new class of ‘Murad’ Stars at L1, possibly ensnaring debris, an asteroid, or small star within a 4-body restricted problem. These three bodies are co-linear. Moreover, osculating or pulsating pulsars raises questions regarding stability of Libration Points except at L1. Here, eigenvalues are extended to include the time rate of change of l. Furthermore, the existence of objects at L1 can account for orbit energy degradations of pulsars such as PSR 1913+16. Such stars could be experimentally found from radio telescopes using signal pulse drifting, nulling, or modulation due to debris reflection or solid blocking from the neutron star beam.