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!

Katie Chamberlain, Christopher J. Moore, Davide Gerosa, Nicolas Yunes.
Physical Review D 99 (2019) 024025.
arXiv:1809.04799 [gr-qc].