Spin contribution to the perihelion precession in binary systems like OJ287: higher order corrections

TL;DR

This paper calculates higher order spin-related corrections to the perihelion precession in binary systems like OJ287 using Schwarzschild and Kerr metrics, expanding in small parameters and comparing with previous results.

Contribution

It introduces higher order correction calculations for perihelion precession considering spin effects in binary systems using advanced metric expansions.

Findings

Derived third-order corrections for perihelion precession

Compared new results with previous calculations

Enhanced understanding of spin effects in relativistic orbits

Abstract

Higher order corrections are obtained for the perihelion precession in binary systems like OJ287, Sagittarius A*-S2 and H1821+643 using both the Schwarzschild metric and the Kerr metric to take into account the spin effect. The corrections are performed considering the third root of the motion equation and developing the expansion in terms of $\epsilon \equiv r_s/\left(a(1-e^2)\right)$ and $\epsilon^{*} \equiv \left(1- \frac{2 \alpha E'}{cJ}\right) \epsilon $.The results are compared with those obtained in a previous paper.