Electromagnetism in Curved Space–Time: Coupling Doppler shifts and gravitational redshifts

We present the basic prerequisites of electromagnetism in flat space–time and provide a description of electromagnetism in terms of the Faraday tensor. We generalize electromagnetic theory to a relativistic setting, introducing the Einstein field equations to describe the propagation of electromagnetic radiation in curved space–time. We investigate the gravitational redshift and derive formulae for the combined effect of the gravitational redshift and the Doppler shift in curved space–time.