If space can expand faster than the speed of light, then are there regions of space with no gravity?
Where there is mass there will be gravity regardless of the speed of light.
Isn't that counter intuitive? If space is expanding faster than mass can propagate that space then there will be no mass in that region and therefore no gravity, correct?
Or gravity is just everywhere?
Space is not expanding into some nowhere. Only the distances between masses expand. So gravitational pulls might decrease but don't vanish.
The space which is expanding includes matter which has mass.
That doesn't make sense though. If I have a cup full of water and then expand the cup to a liter bucket faster than the water can fill the bucket than there will be areas where water doesn't exist.... even if only for a time.
Shouldn't the same apply for gravity?
The cup of water doesn't expand faster than light. Only if you compare it to another cup of water so far away that you can't even see it. (If I have understood the concept of the expanding metric correctly.)
Not sure what relativity has to do with the concept. If you simplify it down to 2 particles (a and b) that are far enough away that space is expanding faster than gravity can cause them to coalesce, will there eventually be a region between them that has no gravity whatsoever? or will it decrease to infinity?
Yes, it has been everywhere from the beginning of time. Essentially, even before matter as we know it existed, there was energy filling all that there is. And all forms of energy gravitate.
I believe the OP is infering a logical need for some kind of unfilled void into which the universe can expand. Scientists widely agree is there is no need or evidence of any 'space' outside the universe. The concept of space without gravity is a more interesting question, but, again, the answer appears to be no. For further discussion see https://einstein.stanford.edu/content/relativity/a11332.html
It isn't. This is a good example of why the "space is expanding" heuristic is misleading. The universe is filled with matter, and continues to be filled with matter as it expands, without any of the matter having to "propagate" anywhere, because there is no "new space" being created that it has to propagate into. All that changes is the average density of the matter (it decreases as the universe expands).
If you have a universe with only two particles, the cosmological models that are sometimes heuristically described as "space expanding" don't apply anyway.
If you just pick out two particles in our actual universe, with lots of other matter in it, then the two particles aren't the only sources of gravity, so the fact that they are far enough apart that each one is beyond the Hubble radius of the other is irrelevant to whether there is gravity between them.
Gravity is a property of space-time. It really doesn't make any sense to say that there are regions of space-time with no gravity. It would be something like saying there are regions of space-time with no space.
TBH, I'm not concerned with whether or not there is an unfilled void in which the universe can expand.
My question applies to the recent discovery of gravitational waves. I am more interested to know if it's possible to differentiate between space and gravity. For instance, oceanic (water) waves are created by energy; however, water can exist without the energy that creates the wave. Can space exist without gravity? or is space synonymous with gravity?
Isn't that just semantics? If you create a universe with the physical constraints of this universe wouldn't the same principles apply?
You shouldn't ask about space, because there is no such thing as "space" in any absolute sense; there is just spacetime. Splitting up spacetime into "space" and "time" requires choosing a coordinate chart, and there is no absolute meaning to coordinates.
In principle, spacetime could exist without gravity, yes, because flat Minkowski spacetime, the spacetime of SR, with no gravity present anywhere, is a possible solution of the Einstein Field Equation. However, there is also no matter or energy in this spacetime. Any spacetime with matter and energy in it will have gravity present--i.e., it will be curved, not flat; this is what the Einstein Field Equation tells us. So as long as matter and energy exist, spacetime cannot exist without gravity.
If there were only two atoms in the entire universe and 100 trillion miles away from each other, would they eventually collide?
It would depend on their initial motions. But they would affect each other gravitationally regardless of whether they eventually collided or not.
So if the space between them expanded exponentially then the effect of gravity wouldn't cease to exist; but would move toward infinity, correct?
Also, is there any proof that gravity isn't just some type of energy that exclusively moves towards to mass?
If there are only two atoms in the entire universe, the cosmological model in which "space expands" does not apply.
Also, what does "move toward infinity" mean?
What does that mean? Are you referring to some known alternate theory of gravity, or is this just your personal speculation? If it's the latter, you should be aware that personal speculations are off topic here.
No. A spacetime with only two particles in it is a different solution of the Einstein Field Equation from a spacetime with two particles plus a lot of other matter and energy. These are physically different configurations and they will exhibit physically different properties.
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