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So from a killing tensor the FRW metric is known to possess, for a massless particle we find the well known result that as the universe expands the frequency of the photons decreases .

But , what does this do for gr ? Was this known to happen before gr ?

Thanks a lot.

(I know it is used to show the universe is expanding etc but is it any sort of test for gr ? )

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    $\begingroup$ It's not clear what you're asking. Note that the development of GR predated the experimental discovery of the red shift. $\endgroup$
    – John Rennie
    Apr 23, 2015 at 9:20

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Yes, it is a test of General Relativity. The red shifts had been observed before . The history is written in the wiki page on Hubble's law. .

Hubble inferred the recession velocity of the objects from their redshifts, many of which were earlier measured and related to velocity by Vesto Slipher in 1917.

The predictions from General Relativity came ten years later:

Although widely attributed to Edwin Hubble, the law was first derived from the general relativity equations by Georges Lemaître in a 1927 article where he proposed the expansion of the universe and suggested an estimated value of the rate of expansion, now called the Hubble constant.

The Big Bang cosmological model incorporates this observation/expectation_from_GR and it is consistent with the observations up to now. So the observed expansion validates General Relativity as a theory .

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