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Speaker |
Laemmerzahl, Claus |
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Co-autors |
Eva Hackmann |
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Talk Title |
Analytical solution of the geodesic equation in Kerr--de Sitter space--times |
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Abstract |
Generalizing our results of the complete analytic solutions of the geodesic equation in Schwarzschild--de Sitter space--time (Phys. Rev. Lett. 100, 171101 (2008) and Phys. Rev. D 78, 024035 (2008)) we here present the complete analytical solution of the geodesic equation in Kerr--de Sitter space--times. Starting with the Hamilton-Jacobi equations we separate the equations of motion. We disuss the effective potential for the $r$-- and the $\theta$--motion which characterizes the shape of the orbits. Using the method of hyperelliptic integrals restricted to the theta--divisor and employing hyperelliptic integrals of first and third kind we can represent the complete set of solutions in terms of Kleinian sigma and related functions. |
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