# Higher-order geodesic deviations and orbital precession in a Kerr-Newman space-time

## TL;DR

This paper introduces a higher-order geodesic deviation method to analyze orbital precession in Kerr-Newman space-times, allowing precise calculations for planetary orbits without relying on Newtonian approximations.

## Contribution

The paper generalizes orbital precession calculations using higher-order geodesic deviations in Kerr-Newman space-times, avoiding Newtonian and post-Newtonian approximations for small eccentricities.

## Key findings

- Accurate orbital trajectories without Newtonian approximations.
- Generalization of perihelion precession in Kerr-Newman space-times.
- Applicable for arbitrary values of GM/RC².

## Abstract

A novel approximation method in studying the perihelion precession and planetary orbits in general relativity is to use geodesic deviation equations of first and high-orders, proposed by Kerner et.al. Using higher-order geodesic deviation approach, we generalize the calculation of orbital precession and the elliptical trajectory of neutral test particles to Kerr$-$Newman space-times. One of the advantage of this method is that, for small eccentricities, one obtains trajectories of planets without using Newtonian and post-Newtonian approximations for arbitrary values of quantity ${G M}/{R c^2}$.