# Analytical Computation of the Perihelion Precession in General Relativity via the Homotopy Perturbation Method

## TL;DR

This paper introduces a novel application of the Homotopy Perturbation Method to analytically compute perihelion precession in General Relativity, providing approximate solutions for planetary orbits in Schwarzschild and Reissner-Nordstrom spacetimes.

## Contribution

It applies the Homotopy Perturbation Method to derive analytical solutions for geodesic equations in spherically symmetric spacetimes, including Schwarzschild and Reissner-Nordstrom metrics.

## Key findings

- HPM solutions closely match known geodesic solutions for Schwarzschild spacetime.
- Derived approximate solutions for charged star spacetime (Reissner-Nordstrom).
- Demonstrated the effectiveness of HPM in solving nonlinear geodesic equations.

## Abstract

We propose a new approach in studying the planetary orbits and the perihelion precession in General Relativity by means of the Homotopy Perturbation Method (HPM).For this purpose, we give a brief review of the nonlinear geodesic equations in the spherical symmetry spacetime which are to be studied in our work. On the basis of the main idea of HPM, we construct the appropriate homotopy what leads to the problem of solving the set of linear equations. First of all, we consider the simple example of the Schwarzschild metric for which the approximate geodesics solutions are known, in order to compare the HPM solution for orbits with those obtained earlier. Moreover, we obtain an approximate HPM solution for the Reissner-Nordstorm spacetime of a charged star.