Higher-order corrections for the deflection of light around a massive object

Abstract

From the Schwarzschild metric we obtain the higher-order terms (up to 20-th order) for the deflection of light around a massive object using the Lindstedt-Poincar\'e method to solve the equation of motion of a photon around the stellar object. Additionally, we obtain diagonal Pad\'e approximants from the perturbation expansion, and we show how these are a better fit for the numerical data. Furthermore, we use these approximants in ray-tracing algorithms to model the bending of light around the massive object.