Hyperelliptic functions and geodesic equations

Abstract

A method for solving geodesic equations in Schwarzschild-de Sitter space-times and higher dimensional Schwarzschild spacetimes is presented. The solutions are derived from Jacobis inversion problem on a Riemann surface of genus 2 restricted to the set of zeros of the theta function, which is called a theta-divisor. In its final form, the solutions are given in terms of derivatives of Kleinian sigma functions.