G V Kraniotis and S B Whitehouse 2003 Class. Quantum Grav. 20 4817 doi:10.1088/0264-9381/20/22/007
G V Kraniotis1 and S B Whitehouse2
Show affiliationsThe 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 Weierstraß Jacobi modular form. The solution is applied to the precise calculation of the perihelion precession of the orbit of the planet Mercury around the Sun.
Issue 22 (21 November 2003)
Received 28 May 2003
Published 6 October 2003
G V Kraniotis and S B Whitehouse 2003 Class. Quantum Grav. 20 4817
Cosimo D'Andrea et al 2003 J. Phys. D: Appl. Phys. 36 1675
F. Camilo et al. 2009 ApJ 705 1
Xueyan Song et al 2002 Supercond. Sci. Technol. 15 511
J L McChesney et al 2002 Nanotechnology 13 545
Magnus T L Hsu et al 2004 J. Opt. B: Quantum Semiclass. Opt. 6 495
Chen Zhi-Zhong et al 2002 Chinese Phys. Lett. 19 375
R Cubeddu et al 2002 J. Phys. D: Appl. Phys. 35 R61
Ulrik L Andersen et al 2002 J. Opt. B: Quantum Semiclass. Opt. 4 S229
N Izadi et al 2010 J. Micromech. Microeng. 20 085041