Post-post-Newtonian light propagation without integrating the geodesic equations

TL;DR

This paper presents a novel derivation of light propagation directions in static, spherically symmetric space-times within the post-post-Newtonian framework, accounting for finite distances of emitter and observer without solving geodesic equations.

Contribution

It introduces a new method to determine light propagation directions in complex space-times without integrating geodesic equations, applicable to finite-distance scenarios.

Findings

Derived propagation directions for finite-distance emitter and observer

Extended the method to rays emitted at infinity

Validated the approach within the post-post-Newtonian approximation

Abstract

A new derivation of the propagation direction of light is given for a 3-parameter family of static, spherically symmetric space-times within the post-post-Newtonian framework. The emitter and the observer are both located at a finite distance. The case of a ray emitted at infinity is also treated.