arXiv subjects

Oleksii Yanchyshen

Publications and source records attributed to Oleksii Yanchyshen.

2 recordsLinked to original sources

arXiv2026

General orbital perturbation theory in Schwarzschild space-time

We derive general relativistic Gaussian equations for osculating elements for orbits under the influence of a perturbing force without any restrictions in an underlying Schwarzschild space-time. Such a formulation provides a way to describe the evolution of orbital parameters in strong gravity relativistic settings. As examples of external forces we considered Kerr and $q$-metric space-times generated forces, for which we solve equations for osculating elements in linear approximation. For the Kerr space-time in the post-Newtonian limit, our result reproduces the well-known Lense--Thirring precession of the longitude of the ascending node.

gr-qc↗

arXiv2024

Gaussian orbital perturbation theory in Schwarzschild space-time in terms of elliptic functions

General relativistic Gauss equations for osculating elements for bound orbits under the influence of a perturbing force in an underlying Schwarzschild space-time have been derived in terms of Weierstrass elliptic functions. Thereby, the perturbation forces are restricted to act within the orbital plane only. These equations are analytically solved in linear approximation for several different perturbations such as cosmological constant perturbation, quantum correction to the Schwarzschild metric, and hybrid Schwarzschild/post-Newtonian $2.5$ order self-force for binary systems in an effective one-body framework.

gr-qc↗