There is another question about this topic, but that is asking about gravitational waves, and I am not. I am specifically asking about the timescale of the merger being finite (actually quick), whereas the black holes (and event horizons themselves) never really form.
There are perfectly good local coordinates in which there merger of two black holes (the formation of a common apparent horizon) happens at a finite time.
And this one:
This isn't some accounting trick, it means we will never see an event horizon form. At this point someone will usually pop up and say that means black holes don't really exist. In a sense that's true in our co-ordinate system, but all that means is that our co-ordinate system does not provide a complete description of the universe.
Now the first one says that the unformed (or not yet formed, because it takes infinite time for them to form) event horizons, merge in a finite time.
The second one says that from our far away view (our reference frame here on Earth), the black holes (and event horizons) never form.
As far as I understand, this means, that from our perspective here on Earth, we have two objects, with not yet formed event horizons, and these merge in a finite time to form a common event horizon. But doesn't this mean that the newly formed common event horizon cannot be formed (when viewed from our frame here on Earth) either?
- If event horizons (black holes) never form in a finite time, then how can they merge to create a common event horizon in a finite time?