I have read this question:
Therefore there is nothing (except things travelling towards the singularity) inside the event horizon of a black hole.
Does anything exist between singularity and the event horizon of a black hole
Now imagine particles moving towards the singularity inside two black holes, that are actually merging. Until the horizons do not overlap, all particles are moving towards the singularity of their own black hole, that is understandable.
Now let's see what happens when the horizons start overlapping. How do particles that are already on the way towards their own singularity, "know" that they need to change course (either towards the other singularity or to a new common one)?
Here is what I do not understand: information inside a black hole can only travel towards the singularity (decreasing r), there is no way for information to travel backwards. Now when the black holes' event horizons start overlapping, naively thinking, the "travel towards the singularity" has to change direction, whatever that direction means, because on this site it is often mentioned that moving towards the singularity is like moving towards tomorrow (so travel in time not space).
Now information can only travel towards a decreasing r, that is equivalently, changes in the gravitational field can only propagate at the speed of light towards a decreasing r. But if that is true, then the particles that are moving towards their own singularity would have to receive information from other regions inside the new common black hole, so that information would need to travel outwards, that is increasing r. But that is not possible, and changes in the gravitational field cannot propagate outwards (increasing r).
So there are two things coming to mind:
particles moving towards their own singularity would need to make a change in direction moving in time as soon as the event horizons start overlapping
to do that, particles would need to receive information (changes in the gravitational field) that is propagating outwards (increasing r) in the new common black hole
- How do particles in merging black holes "know" they need to change direction in time towards a new singularity?