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Gravitational waves originate from significant distances. Presumably they are red-shifted the same amount as the galaxies they originated in. In the absence of gravitational “spectral lines”, can this red shift be measured? And if it can be, is this information useful in calculating distance or inferring the event that created the gravitational waves?

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Gravitational waves should be redshifted.

The gravitational wave signal of an inspiralling binary system, which drifts across a range of frequencies, does not however yield the redshift of the binary system, since changing the redshift is indistinguishable from changing the mass of the system.

In practice, what is usually done is to estimate the redshift from the luminosity-distance, which can be determined purely from the gravitational wave signal (the so-called "standard siren" technique), combined with a cosmological model.

Of course, where there is an optical counterpart - such as a kilonova - then the redshift of the gravitational wave source can then be estimated from its host galaxy. In which case this offers an independent route to determine cosmological parameters.

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There is no reason to suspect that there are no spectral lines at GW. On the contrary: in binary systems like Algol, two stars have been orbiting each other with an almost constant period for millions of years. The frequency change is so small that you would see a clear spectral line if you could receive the emitted GW. There is no problem building a receiver for $f_{GW}=8.073073~\mu$Hz, all that is missing is a suitable antenna.

If the Earth-Algol distance decreases for six months as the Earth orbits the Sun, the reception frequency must be blueshifted. Then follows six months of redshift.

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  • $\begingroup$ "There is no problem building a receiver" there are lots of problems, mostly that the signal is so weak. $\endgroup$
    – James K
    Commented Nov 12, 2023 at 15:53
  • $\begingroup$ @James: No, it's really not difficult. They know exactly how to successfully receive and demodulate the signals from extremely distant probes like voyager. $\endgroup$
    – 9herbert9
    Commented Nov 13, 2023 at 17:28
  • $\begingroup$ Those are em signals. Not the same. $\endgroup$
    – James K
    Commented Nov 13, 2023 at 18:13
  • $\begingroup$ A receiver responds to alternating voltage of a selectable frequency without thinking about the origin of the alternating voltage. The antenna's job is to convert changes in the signal (sound, EM, GW,...) into alternating voltage. $\endgroup$
    – 9herbert9
    Commented Nov 14, 2023 at 10:14
  • $\begingroup$ There's no alternating voltage in a gravitational wave. $\endgroup$
    – James K
    Commented Nov 14, 2023 at 21:11

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