Light Deviation around a Spherical Rotating Black Hole to Fifth Order. Lindstedt-Poincar\'e and Pad\'e Approximations

TL;DR

This paper investigates the deviation of light around a rotating black hole using analytical and numerical methods, providing accurate approximations for small and large angles with novel application of Lindstedt-Poincaré and Padé techniques.

Contribution

It introduces a combined analytical and numerical approach, employing Lindstedt-Poincaré and Padé approximations for precise light deviation calculations in Kerr spacetime.

Findings

Analytical solutions for small deviation angles using Lindstedt-Poincaré method.

Padé approximants improve the convergence of the analytical solutions.

Numerical integration effectively handles large deviation angles.

Abstract

Light deviation around a rotating black hole is calculated using the Kerr metric for both small and large deviation angles. For small angles the Lindstedt-Poincar\'e method is employed to get well-behaved solutions, as well as Pad\'e approximants. For large deviation angles numerical integration has been used.