Effects of rotation and deformation on the orbits of a Kerr-like spacetime

Abstract This study employs an approximate Kerr-like metric with a mass quadrupole perturbation to investigate the equatorial circular motion around deformed, rotating compact objects. The numerical results reveal how the quadrupole modifies the photon sphere and the innermost stable circular orbit, with implications for accretion dynamics near systems such as neutron stars. A stability analysis shows that certain symmetries are preserved in the effective potential, yielding equivalent behavior for co-rotating and counter-rotating particles. Comparisons with the Hartle–Thorne spacetime highlight the influence of higher-order multipole moments. Additionally, under the Black Widow pulsar equation of state, the metric suggests that inspiraling particles may temporarily form a transient, disk-like structure near the pulsar. This would allow interactions between co-rotating and counter-rotating matter. More research is needed to characterize this phenomenon and explore its observational signatures.