Light deflection around a spherical charged black hole to second order. Multivariate Pad\'e approximants

Abstract

From the Reissner-Nordstrom metric we obtain the higher-order terms for the deflection of light around a massive-charged black hole using the Lindstedt-Poincar\'e method to solve the equation of motion of a photon around the compact object. The corrections are performed developing the expansion in terms of $\epsilon=\frac{r_{c}}{b}$ and $\frac{\delta}{b}= \frac{Q^{2}}{6 \pi \epsilon_{0}Mc^{2} b}$. Additionally, from the perturbation expansion, we obtain multivariate Pad\'e approximants. We also show how these are a better fit for the numerical data than the original formal Taylor series.