Relativistic Doppler shift
In a frame with three- velocity (v,0,0) relative to the frequency is . Using the Lorentz transformations we get
so we get the following result:
If , so that the photon moves in the same direction as , we have
For low velocities this reduces to
This is the usual Doppler shift , modified at large v.
If , so the photon moves perpendicular to , we have