Black Hole Spin and Stellar Flyby Periastron Shift

For a scenario of close flyby compact star near spinning black hole, we provide analytical and numerical estimates for the shift trajectory periastron due to relativistic (beyond post-Newtonian) effects. More specifically, derived generalized expression (not limited quasi-circular or elliptical orbits) directly linking spin hole. The permits estimation hole based on astronomical tracking locations stars traveling along highly eccentric (parabolic hyperbolic) trajectories in vicinity We also demonstrate how hyperbolic parabolic may be (temporarily) captured onto orbits around holes, quantitatively examine conditions such scenarios.