Light Deflection around a Spherical Charged Black Hole to Second Order. Multivariate Padé Approximants

From the Reissner-Nordström metric we obtain the second-order terms for the deflection of light around a massive, spherical and charged black hole using the Lindstedt-Poincaré method to solve the equation of motion of a photon around the compact object. The corrections are performed developing the expansion in terms of . Additionally, from the perturbation expansion, we obtain multivariate Padé approximants. We also show how these are a better fit for the numerical data than the original formal Taylor series.