Rotating gravitational lenses: a kinematic approach

Abstract

This paper uses the Kerr geodesic equations for massless particles to derive an acceleration vector in both Boyer-Lindquist and Cartesian coordinates. As a special case, the Schwarzschild acceleration due to a non-rotating mass has a particularly simple and elegant form in Cartesian coordinates. Using forward integration, these equations are used to plot the caustic pattern due to a system consisting of a rotating point mass with a smaller non-rotating planet. Additionally, first and second order approximations to the paths are identified, which allows for fast approximations of paths, deflection angles and travel-time delays.