Light Deviation around a Spherical Rotating Black Hole to Fifth Order: Lindstedt-Poincar´e and Pad´e Approximations

Light deviation around a rotating black hole to Fifth Order is calculated using the Kerr metric for both small and large deviation angles taking into account different spin values (considering direct and retrograde orbits , i.e. co-rotating or counterrotating orbits). For small angles the Lindstedt-Poincar´e method is employed to get well-behaved solutions, as well as Pad´e approximants, then we show that the latter produces excellent results compared to the numerical solutions, thus proving to be a viable method for solving this kind of equations. Our resolution methods produce more accurate results compared to second and third order calculations that appear in the literature. Additionally, the aforementioned are applied to the supermassive OJ 287 and SgrA* black holes considering different impact parameters. For large deviation angles numerical integration has been used.