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?
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If general relativity is exactly correct (in that there lies a point like singularity at the center of a black hole), then the Roche limit of black holes would be zero. Why would it be zero? Because the singularity isn’t a solid sphere. It’s a point of infinite density with a radius of 0. Basically, what this means is that the concept of a Roche limit ceases to exist here.
However, we know that general relativity doesn’t correctly describe reality at the quantum scale. Classical physics (which general relativity is based upon) contradicts quantum physics in many ways. Singularities work at the quantum scale. Singularities of black holes also only interact through gravity. Because gravity is incredibly weak, we have not been able to experiment with it at the quantum scale. So we don’t know how gravity works at the quantum scale yet.
Therefore, we don’t even know if singularities exist inside black holes. Basically, we have no clue about what happens inside black holes, how general relativity and gravity works at small scales and what exactly happens during a black hole merger.
We could answer the above questions after we understand quantum gravity.