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Complete analytic solution of the geodesic equation in Schwarzschild-(anti-)de Sitter spacetimes. (English) Zbl 1228.83023

Summary: The complete set of analytic solutions of the geodesic equation in a Schwarzschild-(anti-)de Sitter space-time is presented. The solutions are derived from the Jacobi inversion problem restricted to the theta divisor. In its final form the solutions can be expressed in terms of derivatives of Kleinian sigma functions. The solutions are completely classified by the structure of the zeros of the characteristic polynomial which depends on the energy, angular momentum, and the cosmological constant.

MSC:

83C10 Equations of motion in general relativity and gravitational theory
83F05 Relativistic cosmology
53C22 Geodesics in global differential geometry
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