Does each solar system have its own individual piece of space-time?

Question

(If you don't want to read all of this, my questions are at the end of this paragraph) This question might get a little confusing for you and me but lets try to answer it. So I've been thinking about how space works and I've manged to understand how every planet is co-planar with its sun and how solar systems are co-planar with their galaxy's black hole but I'm still trying to figure out how space-time works. So lets start here in our solar system, our sun and the planets surrounding it create a curvature in space-time. So that would have to mean space-time is on the same plane as our solar system, right? Well it shouldn't be like that because then all of the universe would be on one plane and all we would see at night its a bright streak in the sky, but all the stars are scattered. So, does this mean each solar system has its own piece of space-time that's on the same plane as itself? Or maybe even each planet has its own piece of space-time that it effects? Please let me know what you think.

? · Answer

Space-time is continuous. There isn't a different space-time around different objects, the space-time has different properties around different objects, including individual planets and every other accumulation of matter such as yourself, but it's still the same grid. The reason that the objects within the solar system are more or less on the same plane is due to the way it formed out of spinning disc of rotating stellar dust. The central star only spins one way in one plane, so that's how the entire disc spins. This has nothing to do with the "type" of space-time our system inhabits. And, in fact, our galaxy is rotating in a completely different plane. Our solar system is like a tilted propeller spinning forward on the galaxy's arm. Other galaxies are spinning in more or less random tilts relative to ours and the galaxy's as well.

? · Answer

Short answer, yes all solar systems are in their own piece of space-time (simply because they are in different places), but no the pieces of space-time aren't separate, and no space-time isn't co-planar with anything at all so far as we can tell (and is not, in point of fact, a plane at all). Space-time isn't like a sheet of paper that you bend to form curvature, and the curvature isn't like the curvature you get when you bend a sheet of paper.
Solar systems and galaxies tend to be co-planar because they form from the same giant clump of gas, which for a number of reasons tends to flatten into a rotating disk that galaxies form out of while still spinning in the same direction. It has nothing to do with space-time, beyond the fact that it would not exist without the space-time that it is in. The "curvature" in space-time is more like squeezing a block of foam; mass pulls at the space around it, compressing nearby space and stretching farther away space and nothing has to be co-planar with anything else.

Does each solar system have its own individual piece of space-time?

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