When 2 black holes approach each other, they both bend space in an opposite direction. There must always be a flat space between 2 colliding black holes.
However, I heard that they actually merge, becoming one...
I wondered, how can this happen?
Also, is it a good way to get very-very close to the center of a black hole by pushing another one close to it, while our probing spacecraft occupies the flat space in between?
EDIT: Obviously, the flat space between the black holes only exists at a single point (L1). But around that point there is a relatively flat space, where a small enough spacecraft can have enough structural strength to survive. Also, around L1, time dilatation is small, so a probe can get out within reasonable time, or can send signals.
EDIT2: Ok, maybe space at L1 is not flat... Let me try to explain what I was thinking:
B1~X~L1~Y~B2
B1,2: black hole1,2
L1: Lagrange 1
X,Y: 2 extreme points on the spacecraft
Forces pulling the spacecraft apart:
F_B1<--X~L1~Y-->F_B2
Forces crushing the spacecraft:
X-->F_B2 ~L1~ F_B2<--Y
Since the forces are equal at L1, pulling apart and crushing should cancel out each other, the closer to L1, the more they cancel.
I wonder if this thinking is wrong because gravity is a pseudo-force, and they cannot simply be added together.
If this is the case, do the tidal forces strengthen or weaken between 2 massive objects?