While it may not be the most common of events, on when Black Holes do find each other and meet, the moments before their union could give us our one and only peek inside a Black Hole. The reason for this must do with their combined center of gravity or Barycenter. A Barycenter is the point between two objects where the gravity of the two objects balances out. At this point of balance, the gravity from both objects is pulling in equal amount but in opposite directions. It is at the Barycenter that there is a very small point of zero gravity.
As two Black Holes approach, even as their event horizons meet, this Barycenter still exists. The event horizon is the total black shell that surrounds a black hole. It is the point when the gravitational pull of a Black Hole becomes too great for even light to escape. In fact, the Barycenter continues to maintain a position between even two massive singularities at the center of joining Black Holes all the way to the point that the two singularities meet and become one.
While some have speculated nothing of significance would happen to as the even horizons of two Black Holes meet, I would argue that instead we would see something very amazing happen. We would see the event horizons of both black holes first pull towards each other under the intense gravitational tidal forces, then as they meet we would see them distort and push away from each other. The reason for this distortion has to do with the Barycenter of the two massive bodies.
When a Black Hole is standing on its own in space, calculating the point of an event horizon is pretty simple. You simple take the mass of the object and apply the gravitational constant along with the distance from the center of the object. A simple equation will tell you when the force of gravity become so great that even light cannot escape and becomes trapped by the gravity of the black hole. Now when you add another Black Hole to the equation, you must take into consideration it’s gravitational pull as well.
Let’s say that you are somehow able to sit in a space ship just inside a Black Hole. You burn your engines at full power in an attempt to fight the pull of the Black Hole. Because you cannot go faster than the speed of light, you can only hope to slow your eventual progress towards the center of the Black Hole. Now imagine another Black Hole comes along and passes very close to the black hole you are trapped on. As the second Black Hole gets closer it’s gravity begins to pull on you as well helping to loosen the grip of the first Black Hole.
Now the total gravity being pulled on you and your space craft is a combination of both back holes. Once the two Black Holes are at equal distances to you, you notice that the gravitational pull has balanced out to zero-G and you can easily escape. You have just become one of the very few lucky ones to have entered the event horizon and lived to tell the tail.