Analytical solution methods for geodesic motion

Understand

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.