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.
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.