Light rays and wave fronts in strong gravity

Accretion onto black holes often proceeds via an accretion disk or a temporary disk-like pattern. Variability features observed in light curves as well as theoretical models of accretion flows suggest that accretion disks tend to be inhomogeneous variety of substructures (clumps) emerge within the flow. Rapid orbital motion of individual clumps then modulates the observed signal in X-rays. Furthermore, changes of spectral lines and polarization properties of the observed signal (or the absence of changes) constrain the models and reveal information about general relativity (GR) effects. In this write-up we summarize the basic equations that have been employed to study light propagation near black holes and to derive the radiation signal that can be expected at a detector within the framework of geometrical optics approximation.