Can gravitational wave be blue/red shifted?

Question

I'm picturing a simple scenario: 2 black holes about to merge and they are receding away from us at constant speed. (I like to negate the rate of expansion of space and assume universe is perfectly flat for now, don't argue with me I'll bite)

Back to my story, I think my hypothetical detector should observe that the wavelength of hawking radiation becoming redder(longer with you will). How about the gravitational wave? I mean how do we know that the gravitational wave is red shifted, in this case the accompanying light cannot testify also there is no way to directly measure it.(don't confuse with gravitational red shift like google or bing usually do, believe me it's utterly annoying to see millions of similar result)

Complimentary question: is there any way to test if the energy of a gravitational wave is quantized?

Answer 1

You can't directly measure the redshift of the gravitational waves in the scenario you suggest. It is degenerate with the estimate of the black hole masses.

What you can estimate is how far away the merging black holes are. That is because the amplitude of the waves is proportional to the reciprocal of distance. You can then use Hubble's law to estimate what the cosmological redshift is.

So I believe the assumption being made (in the recent gravitational wave detection) is that the redshift is entirely due to the expansion of the universe. At $z>1$, that is a very good assumption.

If the source were very nearby and not a merging source -i.e. a binary black hole with a very slowly changing frequency, then in principle you might detect the changing distance as the source moved away as a slowly decreasing amplitude, which would tell you directly that it was receding.