General orbital perturbation theory in Schwarzschild space-time

TL;DR

This paper develops a general relativistic framework for orbital perturbations in Schwarzschild space-time, enabling analysis of orbital evolution under various forces in strong gravity regimes.

Contribution

It introduces a general relativistic Gaussian equation approach for osculating elements applicable to Schwarzschild space-time without restrictions.

Findings

Reproduces Lense--Thirring precession in Kerr space-time in the post-Newtonian limit.

Provides equations for osculating elements under Kerr and q-metric forces.

Offers a new method for analyzing orbital dynamics in strong gravitational fields.

Abstract

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.