Analytical solution methods for geodesic motion

Abstract

The observation of the motion of particles and light near a gravitating object is until now the only way to explore and to measure the gravitational field. In the case of exact black hole solutions of the Einstein equations the gravitational field is characterized by a small number of parameters which can be read off from the observables related to the orbits of test particles and light rays. Here we review the state of the art of analytical solutions of geodesic equations in various space--times. In particular we consider the four dimensional black hole space--times of Plebański--Demiański type as far as the geodesic equation separates, as well as solutions in higher dimensions, and also solutions with cosmic strings. The mathematical tools used are elliptic and hyperelliptic functions. We present a list of analytic solutions which can be found in the literature.

11 pages, no figures; based on presentation at the conference "V. Leopoldo García--Colín Mexican Meeting on Mathematical and Experimental Physics", Mexico City, 2013

References in corpus (1)

• Motion of test particles in a regular black hole space--time

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