We all know Doppler shifts, right? That’s like the biibouuubiiiiboouuuuuu of an ambulance. That happens to gravitational waves as well. Suppose you have a merging binary which is emitting gravitational waves (bibooou). If that binary is going somewhere (say it’s falling into the gravitational potential of a third body), much like the ambulance, the emitted signal will be Doppler shifted. This paper shows a very nice calculation to incorporate Doppler shifts into gravitational waves.
ps. This started out as Katie’s undergraduate summer project at Caltech. Congrats Katie!