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

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.