[evan_au (OP)]

In the region of two merging black holes or neutron stars, Special Relativity predicts that events should appear to be slowed down, as viewed by a distant observer (us). This is due to:
- The objects are in a deep gravitational well
- They are moving very quickly just before they merge (a large fraction of the speed of light)

Several of the recent gravitational wave events have had final frequencies of 400-500Hz.
How much would this have been "red shifted" by the time dilation inherent in escaping from this deep gravitational "hole"?

[jeffreyH]

You would have to know the masses of the two original  black holes first. I do have a text on exact solutions of the Einstein field equations. There may be some information in that if I can find it. I'll post what I find out here.

[jeffreyH]

See here for a discussion of red shift.
https://physics.stackexchange.com/questions/137292/can-gravitational-waves-be-red-shifted

[jeffreyH]

Here is another document with a similar theme.
http://cds.cern.ch/record/570414/files/0207052.pdf

[PmbPhy]

In the region of two merging black holes or neutron stars, Special Relativity predicts ...

General relativity predicts that. No special relativity.

But yes. Special relativistic effects also act on the frequency of gravitational waves. Suppose a gravitational wave is passing by you. It will have a certain frequency. If you changed to another inertial frame moving parallel to the direction of the gravitational wave then you'll measure the frequency of that wave to be different. Whether its higher or lower depends on the direction that your new frame is moving in.


 that events should appear to be slowed down, as viewed by a distant observer (us). This is due to:
- The objects are in a deep gravitational well
- They are moving very quickly just before they merge (a large fraction of the speed of light)

Several of the recent gravitational wave events have had final frequencies of 400-500Hz.
How much would this have been "red shifted" by the time dilation inherent in escaping from this deep gravitational "hole"?
[/quote]

[yor_on]

Not sure about that one if you solely relate it to a time dilation, but you also have to consider the cosmological redshift. That one is about 'inflation' and a subsequent 'accelerating expansion' of the 'universe'. Geometrically we could call it space growing which should lead to all kind of 'waves' becoming diluted, or 'stretched out', as it seems to me.
=

Eh, that was just a answer to the original question btw, and reading the link to stackexchange with the reference to 'gravitational waves' at a Big Bang.

And the idea of time dilated redshifts needs the observer as it is a result of different frames of reference 'interacting' whereas a 'inflation' is decoupled, sort of :), in that it should act equally 'everywhere' the way I think of it.

[Bill S]

……. 'inflation' is decoupled, sort of , in that it should act equally 'everywhere' the way I think of it.

Wouldn’t that apply only if you postulate an “absolute” background to which it can be considered universally “relative”?

[yor_on]

Do you need a background to consider something equal something else, or in this case itself Bill? I don't think I need it myself? That one actually reminds me of Smolin :)

 A absolute background to it would be a trickier proposition

[Bill S]

That one actually reminds me of Smolin

Could be I'm in good company.

I need to think about this a bit.

[jeffreyH]

There is not an absolute background but there is a constant reference. The speed of light in a vacuum. Barring interference all observers will record the same speed. All will agree on the world line of the photon.

[Bill S]

Do you need a background to consider something equal something else, or in this case itself Bill?

I started by trying to get a clear picture of something that might not be equal to itself.  The first example that came to mind was the wind.  It displays very different characteristics in different places; so the wind in Harwich might not be equal to the wind in Chicago, at any given time.  However, at that time, the wind is still, globally, the wind, so must be equal to itself; if that has any real meaning. 

Would the global picture not be a better analogy for inflation?

[Bill S]

There is not an absolute background but there is a constant reference. The speed of light in a vacuum. Barring interference all observers will record the same speed. All will agree on the world line of the photon.

Thanks Jeffrey, I was, ponderously, working towards “c” as a possible factor.  Being a pedant, I’ll still have to work through my lines of reasoning, at some stage, but it can go on “the back burner” for now.