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.