So, I came up with this question which is intriguing me since a bit. Maybe it's stupid, but it's always better to ask.
The question is about inertial reference frames (I'll name them IRF)
We know that the only IRF is the one in which we experience a free fall, hence not subject to any force. If we also look at the laboratory system in free fall, hence accelerating, then one of the two is subject to some force, and we know already that it's the lab system which is "in motion".
So in sooth the free fall IRF is "standing still" and it's the spacetime that falls.
The question is: if the spacetime "falls", does it stretch?
Let's imagine this: let's have two black holes one near another. In both of the IRF we fall in free fall towards the black holes, hence in both cases the spacetimes is falling down towards the black holes.
But if those black holes are very close, let's make the very extreme assumption of few kilometers, does the spacetimes stretch, in the middle?
Will it be "cut"? Or is that a sort of papier-mâché effect that is, the space time will stretch without any rupture?