I From our reference frame, how would a black hole ever form?

[msumm21]

TL;DR Summary

From what I understand, from "our" reference frame a black hole would never form

Looking at Kruskal diagrams, it seems to me we should not be able to see evidence of black holes. Assuming our frame is a hyperbola of roughly constant $r$ in such a diagram, as the black hole's constituent mass comes together time slows (from our POV) to the extent that it never crosses the horizon or forms a black hole.

I realize that, in the frame of a constituent mass, the block hole forms, but my question is from the POV of someone at a roughly constant $r$ outside the black hole.

EDIT: I think my first sentence is mistaken: presumably we could "see evidence" by "watching" the acceleration of an object close to, but outside, the horizon.

 

[PeroK]

It depends what you mean but our POV. It's true that some events cannot be directly observed. And that there are systems of coordinates in which no time can be assigned to a given event. That, however, is a deficiency in the coordinate system. You are free to choose another coordinate system that does include the event under discussion.

 

[msumm21]

It depends what you mean but our POV. It's true that some events cannot be directly observed. And that there are systems of coordinates in which no time can be assigned to a given be event. That, however, is a deficiency in the coordinate system. You are free to choose another coordinate system that does include the event under discussion.

Copy, thanks. I am thinking in our proper time, so in our proper time the BH never forms, right.

Understand your point with some time coordinates it does form.

 

[Nugatory]

I am thinking in our proper time, so in our proper time the BH never forms, right.

"In our proper time" isn't meaningful - better to ask whether an event is or will eventually be in our past light cone, in which case we can reasonably say that "it has happened".

The eternal black hole of the Schwarzschild solution isn't physically realizable, as it describes a black hole that has always existed. A real black hole will have formed by gravitational collapse, and although we cannot directly observe events at the horizon, we can observe that there is a black hole where before there had been some uncollapsed matter..

 

[Dale]

TL;DR Summary: From what I understand, from "our" reference frame a black hole would never form

Looking at Kruskal diagrams, it seems to me we should not be able to see evidence of black holes.

Note that the Kruskal diagram that you posted is for a Schwarzschild black hole. Indeed, you would never see a Schwarzschild black hole form because it does not form. It is pre-existing.

Instead, what you need is the equivalent of a Kruskal diagram for an Oppenheimer Snyder spacetime. The only one I have found is here: https://jila.colorado.edu/~ajsh/bh/collapse.html

in our proper time the BH never forms

Proper time only covers the worldline of the object. So that doesn't make a lot of sense.

 

[PeterDonis]

my question is from the POV of someone at a roughly constant outside the black hole.

See this Insights article:

https://www.physicsforums.com/insights/black-holes-really-exist/