# Higher-order corrections for the deflection of light around a massive object

## TL;DR

This paper derives higher-order corrections to light deflection around massive objects using perturbation methods, improves approximation accuracy with Padé approximants, and applies these to ray-tracing simulations.

## Contribution

It introduces up to 20th-order analytical corrections for light deflection and demonstrates the effectiveness of Padé approximants in modeling gravitational lensing.

## Key findings

- Padé approximants provide better fit to numerical data
- Higher-order terms improve accuracy of light deflection models
- Ray-tracing simulations incorporate these corrections for realistic modeling

## Abstract

From the Schwarzschild metric we obtain the higher-order terms (up to 20-th order) for the deflection of light around a massive object using the Lindstedt-Poincar\'e method to solve the equation of motion of a photon around the stellar object. Additionally, we obtain diagonal Pad\'e approximants from the perturbation expansion, and we show how these are a better fit for the numerical data. Furthermore, we use these approximants in ray-tracing algorithms to model the bending of light around the massive object.