Geodesic equation and theta-divisor

Details Geodesic equation and theta-divisor Geodesic equation and theta-divisor

Mar 2008

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008aipc..977..116h&link_type=abstract

RECENT DEVELOPMENTS IN GRAVITATION AND COSMOLOGY: 3rd Mexican Meeting on Mathematicaland Experimental Physics. AIP Conference P

Physics

2

Einstein-Maxwell Spacetimes, Spacetimes With Fluids, Radiation Or Classical Fields, Riemannian Geometries, Ordinary Differential Equations, Classical General Relativity

Scientific paper

The complete set of analytic solutions of the geodesic equation in Schwarzschild-(anti)de Sitter space-times is presented. The solutions are derived from the Jacobi inversion problem restricted to the set of zeros of the theta function, called the theta-divisor. In its final form the solutions can be expressed in terms of derivatives of Kleinian sigma functions. The different types of the resulting orbits are characterized in terms of the conserved energy and angular momentum as well as the cosmological constant. An elaboration of the necessary steps of the explicit computation of the solutions is given.

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