Geodesic Equations in General Relativity: Motion in Black Hole Space-times with and Without Cosmological Constant

The motions of test particles and light, described within General Relativity by the geodesic equation, are an effective possibility to explore the physics of gravitational fields. Although a majority of gravitational effects can be discussed using approximations and numerics, the appealing goal of a systematic study of all effects can only be achieved using analytical methods. This book is devoted to an extensive study of geodesics in a wide variety of space-times using analytical methods including not only a complete classification of orbit types but also analytic solutions of the geodesic equations. Starting with the static and spherically symmetric Schwarzschild space-time, the geometries become more and more complex, in particular including a cosmological constant. The powerful methods presented here can be used for geodesics in every type D space-time and are applicable to even more general settings.