Unveiling the Formation of Black Holes: A Relativity Perspective

[yprager]

According to general relativity, if a remote observer monitors an object falling onto a black hole, (s)he will never see the moment when the object crosses the event horizon. Due to the time distortion, the falling object will hover over the event horizon forever.

With that in mind, how could the black hole have formed in the first place, in the frame of reference of the remote observer? Wouldn't it take an infinite amount of time for it to form?

 

[phinds]

According to general relativity, if a remote observer monitors an object falling onto a black hole, (s)he will never see the moment when the object crosses the event horizon. Due to the time distortion, the falling object will hover over the event horizon forever.

With that in mind, how could the black hole have formed in the first place, in the frame of reference of the remote observer? Wouldn't it take an infinite amount of time for it to form?

Visually, yes, but remember, the stuff really DOES go in even though a remote observer doesn't see it, so the gravity of the black holes is that caused by the sum of the masses that went in and you really do have a black hole.

 

[PeterDonis]

See this Usenet Physics FAQ article:

http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html

 

[phinds]

Visually, yes, but remember, the stuff really DOES go in even though a remote observer doesn't see it, so the gravity of the black holes is that caused by the sum of the masses that went in and you really do have a black hole.

To expand on this slightly, when I say "you really do have a black hole" I'm referring to the gravitational effects that accrue by virtue of the fact that the matter, in its own reference frame, does fall past EH even though that cannot be "seen" by a remote observer. My understanding is that without sufficient, highly concentrated, mass you can't have an EH and once you have an EH, you have a black hole (or maybe it's that once you have a BH, you have an EH ... they go together).

 

[yprager]

Phinds, thank you for the clarification, but it still doesn't sound particularly convincing to me. Had it taken infinite amount of time for a black hole to form in the remote observer frame of reference -- well, there would have been no black holes in her frame of reference. (Regardless of what happens in the frame of reference of the falling object.) The link provided by PeterDonis sounds more convincing, even though I must admit that I am not fully at ease even with that one.

 

[DrGreg]

Here is a spacetime diagram of a collapse to a black hole, which first appeared in Oppenheimer-Snyder model of star collapse, post #64

Here are some selective quotes from that post:

The pink grid shows the exterior Schwarzschild coordinates. The blue grid shows the interior Schwarzschild coordinates (that is, inside the event horizon, but still outside the collapsing matter). The purple dotted line is the event horizon. The thick blue line is the singularity.

The grey line from the bottom to the left is the border of the vacuum region, i.e. the outermost layer of the collapsing matter.

The pink curves are the worldlines of observers hovering at a constant distance from the centre of the collapsing matter, and the radial pink lines are lines of simultaneity for such observers as determined by the convention of Schwarzschild coordinates. For these observers, none of the events in the blue region occur "simultaneously" with an event on the observer's worldline, so you could say the event "never occurs" (within finite time) relative to that observer. But that is just an artefact of the coordinate system chosen. It's unreasonable to say those events "don't exist".

 

[phinds]

... Had it taken infinite amount of time for a black hole to form in the remote observer frame of reference -- well, there would have been no black holes in her frame of reference...

You miss the point. If the remote observer is dumb enough to fall for an optical illusion, then yes they would conclude that it doesn't exist, and of course it doesn't exist visually for them but if they understand physics, they would conclude, as DrGreg pointed out, that this is just a visual illusion based on their coordinate system and that while the illusion certainly is visually real for them, it does not reflect localized reality at the site of the black hole, just localized reality for them. Cosmology is confusing that way.