http://arxiv.org/abs/1910.01984
We provide new very simple and compact expressions for the efficient calculation of gravitational lens optical scalars for Kerr spacetime. These exact expressions are valid for any null geodesic and can be obtained by recurring to well known results on geodesic motion that exploit obvious and hidden symmetries of Kerr spacetime. These new results for the optical scalars contrast with the rather long and cumbersome expressions previously reported in the literature and constitute a helpful improvement for the sake of an efficient integration of the geodesic deviation equation on Kerr geometry. Also our approach differs with respect to those which try to obtain lens equations adapted to systems with angular momentum by relying on the notion of bending angle and the thin lens approximation such as it is usual done for null geodesics in the weak field regime. However, since the expressions are exact it is worthwhile to remark that the results reported here are valuables also for general lensing analysis such as the studies of caustic structure and the strong field regime, as needed in the calculation of images of supermassive black holes, as well as in computations requiring the angular momentum of the black hole to point in any arbitrary direction. 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. This construction is based on the unique null geodesic passing by the observer and belonging to the \emph{center of mass null geodesic congruence}, instead of the other approaches based on the principal null geodesic congruence frame or coordinate frame. We compare the efficient calculation of weak lens optical scalars with the exact equations; finding an excellent agreement.
E. Boero and O. Moreschi
Mon, 7 Oct 19
35/42
Comments: 17 pages, 11 figures
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