Light bending and perihelion precession: A unified approach

TL;DR

This paper presents a unified, efficient method using the Runge-Lenz vector to derive both light bending and perihelion precession in General Relativity, extending its application beyond Newtonian physics.

Contribution

It introduces a novel, unified approach based on the Runge-Lenz vector to derive key GR effects more efficiently than traditional methods.

Findings

Derivation of GR precession and bending effects using a conserved Newtonian quantity.

Extension of the method to include angular momentum corrections.

Validation of the approach with known results in Schwarzschild geometry.

Abstract

The standard General Relativity results for precession of particle orbits and for bending of null rays are derived as special cases of perturbation of a quantity that is conserved in Newtonian physics, the Runge-Lenz vector. First this method is applied to give a derivation of these General Relativity effects for the case of the spherically symmetric Schwarzschild geometry. Then the lowest order correction due to an angular momentum of the central body is considered. The results obtained are well known, but the method used is rather more efficient than that found in the standard texts, and it provides a good occasion to use the Runge-Lenz vector beyond its standard applications in Newtonian physics.