On the Closed Form Solution for the Geodesics in SdS Space

Details On the Closed Form Solution for the Geodesics in SdS Space On the Closed Form Solution for the Geodesics in SdS Space

2004-02-23

arxiv.org/abs/gr-qc/0402093v4

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Scientific paper

The closed form solution for the geodesics of classical particles in SdS space are obtained in terms of hyperelliptic modular functions and multiple hypergeometric functions. The closed form solution for the five roots of the fifth degree polynomial are found giving the branch places on the genus two Riemann surface. The `Inversion Problem', for the genus two hyperelliptic integral is solved in a closed form. Thus a couple of mathematical problems that have been around for a couple of centuries are solved. The solution is important in astrophysical applications of measuring the cosmological constant.

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