The formation of the event horizon.

[hexexpert]

Assume a spherical region of breathable air just under the density needed to form a low density supermassive black hole. Two people float 20 feet apart from each other exchanging small talk. As gravity does its work, the spherical region holding the person closer to the center reaches the density needed to form a BH. Does the person just outside the just formed event horizon simply see the other person disappear instantly? Before this happens does the further-from-the-center person see a large red shift of the person only 20 feet away. What happens when the other person passes through the event horizon, can he see his friend again?

NOTE: I'm working under the assumption that for supermassive black holes small regions of space won't have extreme curvature and things should appear relatively normal within such a small region.

 

[PeterDonis]

Does the person just outside the just formed event horizon simply see the other person disappear instantly?

No, because he is falling in.

does the further-from-the-center person see a large red shift of the person only 20 feet away

No, because they are both falling in together. Everything looks perfectly normal to them in their immediate vicinity, just as if they were floating in free space in a region of breathable air. Locally they have no way of knowing that the bubble of air they are in has just collapsed within an event horizon and formed a black hole.

I'm working under the assumption that for supermassive black holes small regions of space won't have extreme curvature and things should appear relatively normal within such a small region.

Yes, that's correct.

 

[hexexpert]

Thanks. I was trying for a scenario where the person on the outside, before they also fell in, could relay information from the person on the inside. Just my amateur attempt. :-)

One thing I though might have been novel, as far as thought experiments go, was instead of two people falling into an existing black hole, one after another, was for the black hole to form between the two people, forming "around" one of the two.

But this makes me wonder what happens if you are at the center of this low density gas when one more atom makes the black hole form. In theory, you are NOT dead before it becomes a black hole, but after it forms you just happen to be where the singularity would be. I've seen discussions on falling into a black hole and on down to the singularity but no discussions on what happens if you already were there? Somehow I think you'd end up just waiting to be crushed by the in falling mass.

 

[PeterDonis]

I was trying for a scenario where the person on the outside, before they also fell in, could relay information from the person on the inside.

Unfortunately, that won't work: by the time the person who is higher receives the signal from the person who is lower, he will also have fallen below the horizon. They just have no way of telling this locally.

this makes me wonder what happens if you are at the center of this low density gas when one more atom makes the black hole form

You don't need one more atom. If at one instant the bubble of gas is just a little bit larger than the Schwarzschild radius for its mass, then it can't be static; it must be collapsing. There is a theorem called Buchdahl's Theorem which says that a static object cannot have a radius any smaller than 9/8 of the Schwarzschild radius for its mass. (The reason, basically, is that that is the smallest radius at which pressure can support the object against gravity without going to infinity at the center.) So there is no way to have a continuous sequence of static objects, each slightly more massive, until just adding one atom will make the difference between being a black hole and not. There is a finite range between the radius where the object must start collapsing and the Schwarzschild radius.

In theory, you are NOT dead before it becomes a black hole, but after it forms you just happen to be where the singularity would be.

If you are at the very center, you will eventually be crushed into the singularity; but it will take some time after the event horizon forms before all of the matter reaches the center and crushes you and forms the singularity.