Imagin if entire galaxies were moving faster than the speed of light.

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Hollywood science authorities explain the cause of it all due to Einstein and Lorentz, Dopler and the rest of them dead folks rules, formulas and graphs and the rest. . In other words those folks made the rules and the universe therefore operate that way. You know them graphs and formulas and them tensors and matrices and ... arrays and... oh my.

 

The earth is moving at 1/2 the speed of light wirh respect to galaxies far away. So what?

Bob

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What are the consquences of general relativity, i.e. spacetime curvature moving at half the speed of light?

 

Not much. You seem to be missing the fact that you need two frames of reference before any effect us seen. In the case of the far away stars that are moving away from us at 1/2 the speed of light, MrChips already noted the most visible effect.

Bob

 

What are the consquences of general relativity, i.e. spacetime curvature moving at half the speed of light?

It has no effect on spacetime curvature, only on the relative passage of time between the two frames of reference.

 

Not much. You seem to be missing the fact that you need two frames of reference before any effect us seen. In the case of the far away stars that are moving away from us at 1/2 the speed of light, MrChips already noted the most visible effect.

Bob

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A little stationary rocket does not have spacetime curvature, i.e. gravity around it in any measurable sense to any reference frame. And at any speed of light there is no curvature/gravity move at that speed either.
The far away star or a whole galaxy moving away at some speed of light or faster is a totally a different phenomenon. They are not moving at that speed at all. Whatever space metrics is, that is changing.

In fact the claim is it is due to dark energy etc. So it makes those movement actually the opposite of general and special relativity. The later contracts space and time while the former stretches it back out and them some, except that the spacetime curvature is a local phenomeon basically as far as the vast void of the universe is concerned...

 

I mean what's hard to understand about it? Just draw a spacetime diagram. They take different paths through spacetime. That's it. It's no different than a hypotenuse being longer than a side of a triangle.

EDIT—I'm assuming OP is referring to differential aging, not time dilation, which is coordinate dependent.