This following example explains my question. Let's take a spread out bed sheet, which represents spacetime. At the center of the bed sheet, I start to crumple/wrap the fabric of the bed sheet. The crumpled fabric at the center of the bed sheet represents a planet (or any material object/particle). This idea comes from thinking that matter is mostly, or perhaps as empty as space, and therefore matter could be thought of as crumpled or folded space (spacetime); therefore, in theory, if matter is un-crumpled it will unfold into just space (spacetime). So, in this idea, spacetime = matter. Spacetime or matter are like water. Water can be gaseous or solid. I am sure physicists must have thought about this before, so my question is what have they said about it, and why have they concluded that this is not the case?
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Does this answer your question? Can matter be described as the result of the curvature of space, instead of vice versa? – John Rennie Jan 01 '23 at 09:47
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One can't think of matter as being the same thing as folded space-time, because, matterfield and space-time requires it's own seperate equation of motion: they form a coupled system of equations. If you place a heavy object on the fabric, it will create some local crumpling, which is analogous to Ricci curvature. If you create a wave on the fabric, which is analogous to gravitational waves, then the crumpling resembles Weyl curvature. Weyl curvature exists, even when there is no heavy object locally. However, you shouldn't take this fabric picture too seriously – KP99 Jan 01 '23 at 10:07