Complete analytic solution of the geodesic equation in Schwarzschild--(anti) de Sitter space--times

Understand

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.