Off-equatorial deflections and gravitational lensing in Kerr spacetime and the effect of spin*

Abstract This paper investigates off-equatorial plane deflections and gravitational lensing of both null signals and massive particles in Kerr spacetime in the weak deflection limit, considering the finite distance effect of the source and detector. This is the effect caused by both the source and detector being located at finite distances from the lens although many researchers often use the deflection angle for infinite distances from sources and detectors. The deflection in both the and directions is computed as a power series of and , where are the spacetime mass and source and detector radii, respectively, and is the minimal radial coordinate of the trajectory. The coefficients of these series are simple trigonometric functions of , the extreme value of the coordinate of the trajectory. A set of exact gravitational lensing equations is used to solve for and for given deviation angles and of the source, and two lensed images are always obtained. The apparent angles and their magnifications of these images and the time delays between them are solved. Additionally, their dependences on various parameters, particularly spacetime spin , are analyzed in depth. We find that generally two critical spacetime spin values exist that separate the case of test particles reaching the detector from different sides of the axis from the cases in which the images appear from the same side in the celestial plane. Three potential applications of these results are discussed.