Basically, my question is the title. If a black hole crosses the Roche limit of another black hole, what happens?
For a hypothetical example, let’s say you have a two black holes: one at 5 solar masses and one at 300 solar masses. If the smaller black hole crosses the Roche limit of the larger what happens? Does they simply merge? Would the event horizon of one or both black hole’s be geometrically distorted in some way or retain their spherical shape?
I was curious about the shape of the event horizon part of the question. I don’t know the answer, but this paper makes it clear that a lot of complicated maths is involved, and provides some diagrams that can give you a rough idea of the kind of shapes that might be involved, such as in figure 3 on page 6.