Motion of a vector particle in a curved space-time. III. Development of techniques of calculation

TL;DR

This paper develops mathematical techniques to analyze how a photon's spin influences its trajectory in curved spacetime, extending previous work on first-order corrections in Schwarzschild geometry.

Contribution

It introduces a systematic method to solve the equations governing spin-induced corrections to photon motion in curved spacetime.

Findings

First-order correction to photon geodesic motion derived

Solution obtained via Green function integration method

Framework applicable to spin effects in curved spacetime

Abstract

The studies of influence of spin on a photon's motion in a Schwartzschild spacetime is continued. In the previous paper [13] the first order correction to the geodesic motion is found for the first half of the photon world line. The system of equations for the first order correction to the geodesic motion is reduced to a non-uniform linear ordinary differential equation. The equation obtained is solved by the standard method of integration of the Green function.