First my disclaimer: I am no physicist or scientist of any kind, nor have I had any instruction in these matters by any institute of higher learning. Thus, my grasp of these concepts is going to be dubious at best.
From what I understand gravity warps space itself, especially around super-massive objects like stars. We see light traveling from distant stars change course around planets in a phenomenon called gravitational lensing.
Also, we know from observation of the known universe that the galaxies are all receding from one another which indicates that space is expanding in all directions at all times.
So, my question is:
What happens to the expansion of space in the warped space around large gravitational sources?
You've received some incorrect answers here.
Gravitational fields are infinite in size. But, their strength decays exponentially the further you get from that mass. So, they are only relevant when fairly close to the source, like the moon to the Earth or the solar system to the sun.
So all space is inside gravity wells, and all space expands everywhere.
The thing is, the expansion of space is
extremely tiny. Between any two objects on a planet or something, the amount that space is expanding between them or inside of them, is insignificant compared to other forces that act on them.
Galaxies that are fairly close together can move closer to each other, because the effect of space expansion between them is not as large as the effects of their movement. So, the Milky Way galaxy will collide with our close neighbor, the Andromeda galaxy. Space is expanding between them, but because they're close as far as galactic scales go, the velocity of their movement is much larger than the rate of spatial expansion between them.
But at huge distances, like several billion light years, the expansion of space is pretty much the biggest effect going on. Space expands at a certain rate per unit space, so when there is an astronomically large distance between two objects, they move away from each other very quickly because there is so much spatial expansion between them. Distant objects can even move away from each other faster than the speed of light, because they're not actually moving through space at that speed; just that space itself is expanding between them. That means that even with a lightspeed ship, you couldn't ever close the distance between two galaxies of that distance. The rate of expansion has sometimes been de-accelerating and sometimes been accelerating, due to gravity or dark energy; that's still somewhat of a mystery.
So space expansion is irrelevant on tiny scales (even though it's happening) but totally dominant on the largest of scales.
Earth's gravitation fields expands only so far into space one result holds the moon in orbit. Our sun's gravitational field basically holds the solar system together, space included. The Gravitational field of the black hole in the center of the galaxy holds our galaxy together. I believe that the galaxy as a whole is expanding with the rest of space but am unclear on this point.
Gravity fields are mathematically infinite. It's just that they become exponentially weaker, so after a certain distance things can no longer orbit, and at a further distance it's virtually undetectable due to being infinitesimally weak.
Our galaxy is not really expanding in size, even though space is indeed expanding in the galaxy. At that size, the effects of expansion are small compared to the movements of stars through space, and gravity is the major force going on there, far more relevant than spatial expansion. Maybe in a trillion years galaxies will expand apart because if space keeps expanding and expanding, eventually it'll win, as far as one of the death-of-the-universe theories goes.
How did Hubble manage to observe it, then?
It's observable on the universal scale because the distances are so huge that spatial expansion is dominant.
See, I thought that the expansion of space was supposed to be uniform throughout the universe, and that the increased gravity of dark matter was supposed to explain why the stars in a galaxy don't recede from each other in the same way that galaxies recede from each other due to the expansion of space. If space doesn't expand uniformly, and instead remains static or even becomes compressed around massive objects, then I don't see why dark matter is needed at all.
It expands somewhat uniformly
per unit space (although I'm not 100% sure that's even true, the part about uniformly). Definitely not uniformly between any two objects regardless of distance. Although it's believed that it was once decelerating and now is accelerating, so things like gravity or dark energy seem to affect it. Things that affect the rate of expansion itself are beyond my education.
Two objects a foot apart are only expanding an infinitesimally small amount, and their actual movements for other reasons would totally dominate what positions they have relative to each other.
Stars don't expand away from each other, because the distance between them is not nearly as large as the distance between distant galaxies, and so the movement of the stars through space are far more relevant than spatial expansion between them. Similarly, comets can hit earth and stuff, despite spatial expansion, because they're already fairly close and their velocity is what's relevant. As I said above, even galaxies can move closer to each other if they start close enough.
I described this with an example in a thread years ago, which I'll copy here:
I take a rubber band, and cut it so that it's a single long strand of rubber 10 inches long, and then I place two ants on it. 5 inches from each other. They begin walking towards each other at a rate of 2 inches per second. (So, combined, they become 4 inches closer each second based strictly on walking speed.)
As they do this, I pull the ends of the rubber band to make it stretch. The stretching occurs such that, for each second, each inch of rubber band becomes two inches. So after the first second, the band will be 20 inches, and the second after that, it will be 40 inches, and so forth.
Will the ants ever reach each other? Well, after the first second, the ants went from 5 inches apart to 10 inches apart due to the stretching, but they've each walked 2 inches towards each other, so they've removed 4 inches of distance, and are now a total of 6 inches from each other. In the next second, the 6 inches turns into 12 inches and they've each walked two inches, so they're a total of 8 inches away from each other. It's apparent that the rate of rubber band expansion exceeds their walking pace, and they will never reach each other.
If the ants started closer together, or their walking speed were changed, then they could reach each other. So for instance if they start 3 inches from each other (assuming still 2 inch/sec walking speed), then after the first second the distance expands to six inches but they've each walked two inches towards each other, so now they're only two inches apart. In the next second, that two inches turns into four inches, and they each walk two inches and meet each other. In this scenario, since they started closer together, they reached each other.
Since the rate of expansion depends on the current distance between the two objects (whether it be ants in the example or objects in the universe), the farther apart things are, the faster they expand away from each other.
In that rubber band example, the rubber band expands uniformly everywhere per unit distance, but the rate of expansion between two objects on that rubber band will depend very much on how far apart they currently are.
Stars can move towards other stars because like the close ants, they start close enough that the rate of expansion per unit space isn't that fast. That's of course true for any objects in the solar system, or on earth, or in your living room. The amount of space you're starting with is tiny, so the total amount of expansion is tiny.
Close galaxies can still reach each other. Distant galaxies are like those ants that started farther apart. Space expands per unit space, so once they're far enough apart, even if they're moving through space towards each other, the amount of spatial expansion between them is larger, so they'll never reach each other and instead will continue to expand away from each other.
