B Does Space Recover or Oscillate After Being Distorted by Massive Objects?

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    Fabric of space
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The discussion centers on whether space returns to its original state or oscillates after being distorted by massive objects. It highlights that spacetime is a four-dimensional geometric structure, not a tangible "fabric," and emphasizes the importance of time in understanding gravitational effects. The conversation critiques the metaphor of "fabric" as inadequate for describing spacetime and clarifies that gravity is inherently linked to the geometry of spacetime. Additionally, it questions the interpretation of gravitational wave animations, suggesting they may not accurately represent spatial changes. Overall, the nature of spacetime and its response to massive objects is complex and not easily visualized.
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When a massive object travels through space distorting its geometry, does the space gradually revert to its previous state, or does it oscillate back and forth eventually settling into its state as it was before it was distorted by the massive object ?
If the fabric of of space has a high tension value, then this would be a lot of energy added to space and might affect Hubbles constant ?
When watching the LIGO recording of two black holes merging, could the end of the gravitational wave recorded be from the fabric of space reverberating.
 
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There is no "fabric" of spacetime. Spacetime is geometry. It's where things happen, not a thing itself.
 
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Neither. It is simply not how things work. Furthermore, gravity is the geometry of spacetime, not space. The time part is extremely important.
 
Unfortunately, "fabric" is a metaphor, and quite a poor one.

Relativity models spacetime, not space. Spacetime is a 4d structure, and to get what we call "space" from it you have to (mathematically) slice it into a stack of 3d sheets, analogous to slicing a block of cheese into a stack of 2d slices. Each slice is "space at one instant", and the notion of the geometry of space changing with time comes from looking at each successive slice, not from any single thing changing. Furthermore, as Orodruin notes, quite a lot of the important curvature lies in planes orthogonal to any such slicing and is lost in this visualisation.

The animations of gravitational waves that I've found on a quick search describe themselves as showing "the strength of curvature", so I doubt they're even direct representations of any choice of space. They're likely plots of some summary parameter like the Kretchmann scalar.
 
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Being material observers, we do not expand with the universe. Our ruler for measuring its increasing size does not expand either - its scale does not change. If I identify the ruler with a metric, then from my perspective it should be invariant both spatially and temporally. If it expanded with the universe, then its size measured with this ruler would be constant. Why then do we use a metric with the spatial scale expanding with the universe and constant temporal scale to measure the...

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