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?
The roche limit usually just refers to the effects of gravity upon a smaller object, and how it can potentially break it up in orbit. For black holes it’s not really the same effect. The only thing that does affect black holes is the moment their event horizons touch, which then drags the smaller black hole into an inevitable merger of the two.