Analytic solutions of the geodesic equation in axially symmetric space-times

Abstract

The complete sets of analytic solutions of the geodesic equation in Taub--NUT--(anti-)de Sitter, Kerr--(anti-)de Sitter and also in general Plebanski--Demianski space--times without acceleration are presented. The solutions are given in terms of the Kleinian sigma functions.

4 pages, 4 figures, accepted for publication in EPL

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• Using LISA EMRI sources to test off-Kerr deviations in the geometry of massive black holes
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• On conformal Killing-Yano tensors for Plebanski-Demianski family of solutions

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