Since Black Holes (BH) cannot be observed directly, one can only infer their presence through their influence on the motion of other objects or on the propagation of light or - as shown recently - through gravitational waves created by binary BH systems. Examples for the first cases are the stars orbiting the BH at the center of our Milky Way, the accretion disks around BHs and jets launched from BHs, or the expected observation of the shadow of a supermassive BH like SgrA* or M87. In most cases the stars - ordinary neutron stars, pulsars or magnetars - can be very well approximated by a point mass obeying the geodesic equation. Near the gravitating body, however, the extension of the stars as well as their rotation may influence the orbit. This is described by the Mathisson-Papapetrou-Dixon equations. Also, additional matter near a BH like a star cluster or a massive accretion disk has influence on the motion of the star under consideration. A further phenomenon near BHs is the so-called Aschenbach e ffect where the azimuthal velocity is no longer a monotonic function of the distance from the gravitating center, which is therefore a purely relativistic eff ect. This has been applied to accretion disks and has also been slightly generalized to other cases like naked singularities. It is also interesting to investigate the relativistic version of the Roche lobe which describes the domain of influence of two gravitating bodies in a binary system.

All these eff ects can be treated in standard Kerr spacetimes in order to obtain the physical properties, such as mass and spin, of the gravitating body, or in more general spacetimes, thus aiming at extracting phenomena which can be used for testing GR and the physics of BHs. Regarding the latter one can inverstigate effects for regular BHs or objects mimicking BHs, and test the no-hair theorem or the cosmic censorship conjecture.

Ultimately, where possible the above effects will be described in analytic timing formulae, allowing realistic simulations of future observational tests and thereby preparing the data-analysis tools for the time when the first pulsar orbiting a black hole will be discovered.