Light deflection around a spherical charged black hole to second order. Multivariate Padé 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-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 $\epsilon =\frac{r_c}{b}$ and $\frac{\delta }{b}=\frac{Q^2}{6\pi {\epsilon }_{0}M{c}^{2}b}$. 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.

32 pages, 8 figures. arXiv admin note: text overlap with arXiv:1701.04434