Space itself is expanding on very large scales. But since space and mass influence each other, I wondered if an expansion of space could also occur on smaller scales, given the right circumstances. Since massive bodies locally curve spacetime, I think that the space between two bodies might "relax" if these bodies are moving away from each other.
So, if two massive bodies move through space away from each other, does this also cause a metric expansion of space in between them?
My feeling is that it should, but I also know that general relativity can be tricky...
Update: To clarify, I was thinking about two distant bodies that are not tightly bound by gravitation or other forces. Let's say there is an empty patch of space in the universe with only two distant galaxies or two distant black holes in it that are moving away from each other due to some initial motion. Even though the gravitational attraction between them is very small due to the large distance, does the increasing distance between the two bodies also cause a (very small) metric expansion of space?