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Dynamics of Apsidal Motion in Non-Synchronous Binary Pulsars Coupled Orbit and Spin Evolution

The apsidal motion of a non-synchronous binary pulsar serves as a valuable probe of relativistic gravity, stellar stricture, and dynamical evolution of close binary systems, In this study, we investigate the combined influence of general relativity, stellar oblateness and tidal interaction on the apsidal motion of three binary pulsars: 1913+16, J0737-3039A/B, and J0621+1002. Zahn's tidal equations \cite{1977A&A....57..383Z, 1989A&A...220..112Z} were employed for numerical integrations to describe tidal effects and their role in orbital and spin evolution. We estimated the timescales for tidal synchronization and orbital circularization for each system. The results indicate that tidal effects play only a minor role in orbital decay compared with energy loss due to gravitational wave emission. This is evident in the compact system PSR 1913+16, where the orbital period decreases by approximately 76.5 $μ$s/yr as a result of gravitational radiation. The double pulsar J0737-3039A/B exhibits faster orbital evolution, with synchronization occurring in about 8.4$\times10{^3}$ years, whereas the wider system J0621+1002 shows negligible orbital change over timescales exceeding 10$^{10}$ years. The simulations demonstrate clear trends of decreasing semi-major axis and eccentricity, accompanied by an increase in spin rate among the binary pulsars studied. The derived apsidal motion constants [$k\simeq0.1$] are consistent with theoretical expected values, and the corresponding tidal friction times (between a few hours to several days) agree well with theoretical predication. These results emphasize the dominant role of relativistic effects in neutron star binaries and highlight the importance of including gravitational-wave terms long-term orbital evolution