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

TL;DR

This paper derives and solves in closed form the relativistic orbital perturbation equations in Schwarzschild space-time using elliptic functions, considering various perturbations relevant to astrophysics and fundamental physics.

Contribution

It introduces a novel analytical approach to orbital perturbations in Schwarzschild space-time using Weierstrass elliptic functions, including solutions for multiple perturbation types.

Findings

Analytical solutions for orbital perturbations in Schwarzschild space-time.

Application to cosmological constant, quantum corrections, and self-force effects.

Enhanced understanding of relativistic orbital dynamics.

Abstract

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.