Abstract

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

Highlights

  • The sequence of steps in the analytical approach is the following: (a) we start with articulation of the principle of least action within a specific structure of spacetime in the vicinity of a spinning black hole; (b) we construct the Lagrangian for the test body of finite mass; (c) we find equations of motion for the body; (d) from the symmetry of the Lagrangian, we find the integrals of motion; (e) we obtain the key equation for the trajectory, which captures the nonlinear general-relativistic effects

  • In this paper, we provide (1) analytical expressions for the periastron coordinate (Ψ) for an elongated trajectory; (2) numerical simulations and qualitative examinations of several illustrative scenarios; (3) discussion of the theoretical method permitting such comprehensive consideration; (4) illumination of the importance of symmetries of the Lagrangian and their contribution to construction of solutions; (5) illustration of the possibility of arising resonance regimes when test-bodies move in the vicinity of black holes

  • It is shown that stars with the initial values of angular momentum (j0 ) that are less than√certain critical value become captured by the black hole, while the stars with j0 > jc have their trajectories distorted by the black hole in various ways, but eventually return to infinity

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