ANALYTIC SOLUTION OF GEODEISC EQUATIONS IN HIGHER DIMENSIONAL SPHERICALLY SYMMETRIC SPACE-TIMES

With a new method based on the theory of hyperelliptic functions we solve geodesic equations in higher dimensional spherically symmetric space-times: Schwarzschild (9,11), Schwarzschild-de Sitter (9,11), Reissner-Nordström (7) and Reissner-Nordström-de Sitter (4,7). The equations of motion in the considered space-times contain the underlying polynomial of degree 5 or 6, corresponding to a genus 2 curve.