Astronomy and Astrophysics – Astrophysics
Scientific paper
2003-05-12
Class.Quant.Grav. 20 (2003) 4817-4835
Astronomy and Astrophysics
Astrophysics
LaTeX file, 24 pages, substantial changes following the Referees' recommendations. Accepted for publication in Classical and Q
Scientific paper
10.1088/0264-9381/20/22/007
The geodesic equations resulting from the Schwarzschild gravitational metric element are solved exactly including the contribution from the Cosmological constant. The exact solution is given by genus 2 Siegelsche modular forms. For zero cosmological constant the hyperelliptic curve degenerates into an elliptic curve and the resulting geodesic is solved by the Weierstra$\ss$ Jacobi modular form. The solution is applied to the precise calculation of the perihelion precession of the orbit of planet Mercury around the Sun.
Kraniotis G. V.
Whitehouse S. B.
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