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

作     者：Carlos Rodriguez Carlos Marín 

作者机构：Department of Physics Universidad San Francisco de Quito Quito Ecuador 

出 版 物：《International Journal of Astronomy and Astrophysics》 (天文学与天体物理学国际期刊（英文）)

年 卷 期：2018年第8卷第1期

页      面：121-141页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Light Deflection Black Hole Padé 

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.