Spacetime "curvature factor" by a specific mass

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Is there an attribute of spacetime that determines the curvature that will be caused by a specific mass thus resulting to the corresponding gravity?
In other words: can there be "harder" or "softer" regions of spacetime where the same mass will bend spacetime less or more thus resulting to less or more gravity?
 

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Orodruin
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No. Space-time curvature is governed by the Einstein equations, which are the same everywhere.
 
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Can there be? Yes, there could. We haven't observed the behavior of every single region of spacetime in the entire history of the universe, so we cannot definitively say that no region of spacetime behaves that way.

Are there? We've observed gravitational phenomena from the scale of small objects on earth (google for "Eotvos" and "Pound-Rebka") all the way up to the motion of galactic clusters and we have not found the tiniest trace of such an effect. Furthermore, our best current theories (quantum mechanics and general relativity) don't give us any reason to expect to find such a thing.

So the best answer to your question is "almost certainly not".

I do have to point out that your question is a bit like asking whether there are zebras in Antarctica. We haven't looked everywhere in Antarctica, so there might be zebras somewhere there; but we've never seen any evidence of zebras in any of the parts of Antarctica that we do know about; and current theories of biology give us no reason to think that there might be zebras in Antarctica.
 

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