Refinements and corrections to the deflection angle of light in Kerr-de Sitter spacetime

Abstract

The deflection angle of equatorial light (the light in the equatorial plane) in Kerr-de Sitter (KdS) spacetime was previously calculated by Sultana [\href{https://journals.aps.org/prd/abstract/10.1103/PhysRevD.88.042003}{Phys. Rev. D 88, 042003 (2013)}]. However, we have identified three problems with his result: (a) Orbit problem, the orbit solution used for computing the deflection angle is inaccurate as it does not stem from the original equation of motion (EOM). (b) Position problem, assuming the source and observer are at infinity is physically unrealistic given the presence of the cosmological horizon. (c) Static problem, assuming the observer remains at rest in a static slice of spacetime ignores the expansion of the de Sitter space. In this paper, we address and correct these issues respectively by (a) deriving the orbit solution through solving the original EOM directly, (b) employing a widely accepted definition of the finite-distance deflection, and (c) adopting the Randers optical space for the spatial projection of null geodesics. Based on these corrections, we obtain a more precise and applicable result for the deflection angle of equatorial light in KdS spacetime.