Analytical solution methods for geodesic motion

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 Pleba\'nski--Demia\'nski 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.Comment: 11 pages, no figures; based on presentation at the conference "V. Leopoldo Garc\'ia--Col\'in Mexican Meeting on Mathematical and Experimental Physics", Mexico City, 201

On the interpretation of Michelson-Morley experiments

Recent proposals for improved optical tests of Special Relativity have renewed interest in the interpretation of such tests. In this paper we discuss the interpretation of modern realizations of the Michelson-Morley experiment in the context of a new model of electrodynamics featuring a vector-valued photon mass. This model is gauge invariant, unlike massive-photon theories based on the Proca equation, and it predicts anisotropy of both the speed of light and the electric field of a point charge. The latter leads to an orientation dependence of the length of solid bodies which must be accounted for when interpreting the results of a Michelson-Morley experiment. Using a simple model of ionic solids we show that, in principle, the effect of orientation dependent length can conspire to cancel the effect of an anisotropic speed of light in a Michelson-Morley experiment, thus, complicating the interpretation of the results.Comment: To appear in Phys.Lett.