Higher-Order Corrections for the Deflection of Light around a Massive Object. Diagonal Padé Approximants and Ray-Tracing Algorithms

摘要

From the Schwarzschild metric we obtain the higher-order terms for the deflection of light around a massive object using the Lindstedt-Poincaré method to solve the equation of motion of a photon around the stellar object. The asymptotic series obtained by this method was obtained up to order 20 in the expansion parameter, and was found to better approximate the numerical solution with higher order terms—a property that can’t be taken for granted for any asymptotic series. Additionally, we obtain diagonal Padé approximants from the perturbation expansion, and we show how these are a better fit for the numerical data than the original formal Taylor series. Furthermore, we use these approximants in ray-tracing algorithms to model the bending of light around massive objects.