Questions About Gravitational Waves

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Ontophobe
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1. If the Michelson-Morley experiment were to be conducted with gravitational waves instead of light waves, would the results be any different?

2. Ought we to expect the existence of "gamma" gravitational waves and "radio" and "microwave," etc. gravitational waves? In principle, could there be a "gravitational microwave background?"

3. Corollary to #2: Ought we to expect gravitational waves to undergo Doppler effects?

4. Back when we thought light moves through an ether, we hypothesized (based on the nature of light) that the ether must be something akin to a really rigid glass. We no longer believe in the ether, but we do believe in a "spatio-temporal fabric" (tomayto/tomahto) through which gravitational waves move. Given the nature of gravitational waves, to what material substance would we compare the fabric of space-time? Glass? Rubber? Water?
 
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Ontophobe said:
If the Michelson-Morley experiment were to be conducted with gravitational waves instead of light waves, would the results be any different?

Yes, you will have a very hard time finding a gravitational beam splitter and a gravitational wave mirror. You simply cannot do the MM experiment with gravitational waves as they will go right through your experimental setup.

Ontophobe said:
2. Ought we to expect the existence of "gamma" gravitational waves and "radio" and "microwave," etc. gravitational waves? In principle, could there be a "gravitational microwave background?"
Yes, gravitational waves can have different frequencies. Different frequencies of gravitational waves are predicted by different phenomena. Gravitational waves from the very early Universe would essentially probe the physics of inflation and not be due to a thermal background.

Ontophobe said:
but we do believe in a "spatio-temporal fabric"
No we don't. This is just a popularised figure of speech to describe what is really going on in the theory. The rest of this question therefore makes no sense.
 
So gravity waves aren't waves in space-time, in contrast to EM waves which are waves in a field of potentials in space-time? Space-time isn't actually a thing (albeit non-material)? With what should I replace this popularized fiction?