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

## TL;DR

This paper derives higher-order light deflection terms around a charged black hole using perturbation methods and introduces multivariate Padé approximants that better fit numerical data than Taylor series.

## Contribution

It develops second-order corrections for light deflection around a charged black hole and introduces multivariate Padé approximants for improved data fitting.

## Key findings

- Second-order light deflection terms derived
- Multivariate Padé approximants outperform Taylor series in data fitting
- Enhanced understanding of light behavior near charged black holes

## 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.