Geodesic Geometry of Black Holes

A geodesic is a curve that its tangent is transported parallel with it. In this monograph it is explained how geodesics are classified, described methods of finding solutions of equations by which geodesics are governed, and illustrated orbits derived on the basis of these solutions. In this book null, space-like and time-like geodesics are studied in the case of the space-times of Schwarzschild, Reissner-Nordstr"om and Kerr black holes. A thorough treatment of the space-like geodesics of the Schwarzschild solutions has been given. These geodesics are the trajectories of Tachyons (faster than light particles) and are treated in a complete manner. This has been done by obtaining exact solutions and solving them numerically. All solutions for geodesics for a Reissner-Nordstr"om black hole have been given in complete detail, i.e. time-like, null and space-like geodesics and orbit of a charged particle. Equatorial geodesics of all three types of the Kerr black holes are considered ("slow Kerr", "extreme Kerr", and "fast Kerr"), and few examples of orbits out of equator are here, too.