Line emission from accretion discs around black holes: the analytic approach

The broad X-ray iron line observed in many active galactic nuclei spectra is thought to originate from the accretion disc surrounding the putative supermassive black hole. We show here how to perform the analytical integration of the geodesic equations that describe the photon trajectories in the general case of a rotating black hole (Kerr metric), in order to write a fast and efficient numerical code for modelling emission line profiles from accretion discs.