Efficient gravitational lens optical scalars calculation of black holes with angular momentum

Abstract

We provide new very simple and compact expressions for the efficient calculation of gravitational lens optical scalars for Kerr spacetime which are exact along any null geodesic. These new results are obtained recurring to well known results on geodesic motion that exploit obvious and hidden symmetries of Kerr spacetime and contrast with the rather long and cumbersome expressions previously reported in the literature, providing a helpful improvement for the sake of an efficient integration of the geodesic deviation equation on Kerr geometry. We also introduce a prescription for the observer frame which captures a new notion of \emph{center of the black hole} which can be used for any position of the observer, including those near the black hole. We compare the efficient calculation of weak lens optical scalars with the exact equations; finding an excellent agreement.