I have read this question:
What I have not seen is a purely classical argument for the non-separation of a black hole merger. One can obviously take the time reversed spacetime manifold of a merger and get a valid manifold that splits - but this is a black hole disturbed by a complex ingoing set of strong gravitational waves that splits, a bit like how a loud crash sound converging on some shards can in principle make them reassemble into a vase jumping back up on a shelf. Possible, but thermodynamically impossible.
If you mean overlap, and if you are asking if it's possible that merging can be avoided even if the event horizons of both black holes were to overlap, then the answer is still no. They will merge (regardless of how fast the black holes are moving). The escape velocity at an event horizon is equal to the speed of light, and nothing (with mass2) can have this speed, so even if two black holes approach with a great speed, they will merge if their event horizons overlap.
Imagine a setup where two black holes of similar size and energy moving both at relativistic speeds, but in opposite directions so, that when they pass by, their event horizons slightly overlap. Now as far as I understand, gravitational fields here are extremely strong, but not infinitely strong. In my understanding, the kinetic energy of the black holes could overcome the gravitational attraction, and even if the event horizons (which are not physical objects, but just boundaries) slightly overlap, the black holes themselves could continue their way in the opposite directions, and separate the event horizons again (maybe by exchanging part of their energies, so that they change mass).
The first answer says so (it is possible), and the second answer only applies the speed of light limit to say no. The second one is arguing about the escape velocity, but that is not what I am asking about. I am not denying that the horizons will inevitably overlap. I think it is a given that the effects of gravity travel at the speed of light (faster then the black holes), and the horizons will overlap. But just because two boundaries overlap where the escape velocity is exceeding the speed of light, why would that affect the whole objects' (black holes) interior completely? Just because the two boundaries overlap (meaning a partial unification), that does not necessarily mean that the interiors of the objects will completely unify. The rest of the objects could have kinetic energies that overcome gravity. I believe that it is not correct to think that black holes are some kind of rigid solid objects (where if the boundaries touch it will grag the whole object inevitably), whereas in reality they are objects like stars but with a boundaries that signal the extreme gravitational field. Extreme does not mean infinitely strong, that is very important. What I am asking about is the possible domination of the kinetic energies over the attraction of gravity.
So there are two thought coming to mind:
black holes are not solid rigid objects (we are not talking about two billiard balls touching). Why would the overlap of boundaries drag the whole object inevitably? Are we realistically saying that two black holes would slow down in a matter of seconds from 0.9c to close to 0 (or possibly go into a spiral)?
gravity is extreme, but extreme does not mean infinite. Kinetic energies could dominate gravity.
Just to clarify, I am asking whether the kinetic energies of the black holes could be enough to overcome the attraction of the gravitational fields, and yes, especially in the case when the horizons slightly overlap. The gravitational fields of the black holes is not infinitely strong. Theoretically, the kinetic energies of the black holes could overcome this. So no question, the horizons will overlap, and maybe the two black holes will exchange energies, and change mass, but could depart and continue on their opposite ways.
- Can two relativistic black holes' event horizons overlap and separate again?