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This question already has an answer here:

When large planetary objects moves, it bends spacetime according to the mass this object has. The question is: when large celestial object moves away from say point A, - how does spacetime "knows" what curvature it had before, so it can bent itself back to however curved it was before.

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marked as duplicate by Pulsar, Jon Custer, Sebastian Riese, ZeroTheHero, glS May 9 '18 at 11:33

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The curvature of spacetime is governed by the Einstein field equations. The solution of this equation solves the metric and with that the curvature of spacetime.

In case all mass is so far away that it's effects can be neglected you will end up with flat spacetime. In other words the 'usual' metric diag(-1,1,1,1) we all know and love from special relativity.

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  • $\begingroup$ Let's take Earth travelling around the Sun. At any given moment Earth moves into a next point of its orbit, the mass of the Earth is what makes space time to be bent. When Earth leaves say point A and comes to point B, the space time in point A should restore itself to a relatively flat state, exactly as it was before the Earth moved into point A. how does space in the point A "knows" what degree of flatness it had before Earth moved into the point A??? $\endgroup$ – Guerra Liberrta May 6 '18 at 21:27
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    $\begingroup$ This isn't correct. Gravitational waves and black holes are both vacuum solutions of the Einstein field equations. $\endgroup$ – Ben Crowell May 6 '18 at 23:32
  • $\begingroup$ I know it, but I don't love it. But, as @BenCrowell said, the solutions being discussed are vacuum solutions of the EFE, they are not the trivial Minkowski spacetime solutions! $\endgroup$ – Dr. Ikjyot Singh Kohli May 6 '18 at 23:41

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