On the frequency shift in radiation from a source orbiting a balckhole

Abstract

An analytical study has been carried out of the non-tangential emission of photons in the orbital plane from a monochromatic source of radiation orbiting a blackhole, using the method of geometrical optics. The formulation is applicable to eccentric orbits. The frequency shifts in radiation, which is a combination of Doppler effect and gravitational redshift, is studied for various angles of emission. For compact orbits, the analysis predicts, purely on geometrical grounds, features which may be of astrophysical interest, namely, the spectral line broadening with an asymmetrical profile in the case of a stellar-mass blackhole and peculiar line oscillations in the case of a supermassive blackhole.