Event Horizons / Time Dilation

[paulctan]

Forgive me if I'm being naive or if this has been answered before, but, I was wondering if someone can explain to me the formation of the event horizon on a black hole.

Premise:

As a star collapses, the gravitational force increasing as the volume decreases (i.e. density increases).

As gravitational forces increases, the time dilation effect increases.

My question:

As the star collapses to the point where it's density is sufficient to create an event horizon, won't objects falling into the star (remaining stellar matter, etc.) start to be affected by the time dilation, therefore to the outside observer, we would see all the matter in the star frozen in time (i.e. NOT moving) just before the event horizon?

Would that not also mean that we would not really see a black hole being invisible, but rather a dark hole with the remaining stellar matter reflecting light (albeit massively red-shifted) back out as a shell around the event horizon?

Would this also mean that a singularity actually never forms in the lifetime of our universe? I.e. we would never hope to be able to observe a singularity because the time dilation effect would never pull in the remaining matter that is stuck at the event horizon?

Doesn't this mean that all the talk about naked singularities and spinning black holes are meaningless because the matter never collapses into a infinite dot of infinite density?


If someone could enlighten me on why I'm misguided, please do so!

Thanks.

Paul Tan.

 

[JesseM]

See this page of the Usenet Physics FAQ, especially the section with the heading "Won't it take forever for you to fall in? Won't it take forever for the black hole to even form?"

 

[paulctan]

JesseM: Thanks for the quick response.

I just read the FAQ link you posted, but the link states the viewpoint of the object falling into a black hole. I agree that to that object, time would pass normally.
However, wouldn't the rest of us NEVER see the object even hit the event horizon? Therefore, for us, in the lifetime of our universe, we will NEVER see a formation of a singularity because in our time frame it will take an infinite amount of time for any object to approach the event horizon?

Therefore wouldn't we never have black holes, but just dark shells? (ok, maybe really dark shells).

However, my point is that a singularity actually never really forms in the timeline of our universe because of infinite time dilation.

Please enlighten me... thanks.

Paul Tan.

 

[JesseM]

JesseM: Thanks for the quick response.

I just read the FAQ link you posted, but the link states the viewpoint of the object falling into a black hole. I agree that to that object, time would pass normally.

Did you read the whole thing? The section I said to look at, "Won't it take forever for you to fall in? Won't it take forever for the black hole to even form?", deals specifically with what would be seen by external observers.

 

[paulctan]

Did you read the whole thing? The section I said to look at, "Won't it take forever for you to fall in? Won't it take forever for the black hole to even form?", deals specifically with what would be seen by external observers.

Yes, I did real the whole FAQ. The FAQ does indeed state that we will see the person falling into the black hole stop at the event horizon (actually it state that we will not really even see them as they will be very much redshifted to darkness). That point precises adds to my argument that singularities actually never form in the timeline of our universe. Therefore all the theorizing about what happens at infinities of the singularities actually never applies in our reality.

Please tell me that I am wrong because I seem to have reached a different conclusion than that of all the top physicists working on singularities. I must really be missing something fundamental, and if you could enlighten me, I would really appreciate it!

Paul Tan.

 

[paulctan]

Specifically, this quote in the FAQ distubs me:

"So if you, watching from a safe distance, attempt to witness my fall into the hole, you'll see me fall more and more slowly as the light delay increases. You'll never see me actually get to the event horizon. My watch, to you, will tick more and more slowly, but will never reach the time that I see as I fall into the black hole. Notice that this is really an optical effect caused by the paths of the light rays."

The part about it being an optical effect is troublesome. I assert that it is not an optical effect, as we have proven the time dilation effect of gravitational fields to be real and not just an optical illusion. (i.e. do the though experiment of a spaceship just skimming the gravitational field of a black hole would effectively travel to the future).

Paul Tan.

 

[JesseM]

Specifically, this quote in the FAQ distubs me:

"So if you, watching from a safe distance, attempt to witness my fall into the hole, you'll see me fall more and more slowly as the light delay increases. You'll never see me actually get to the event horizon. My watch, to you, will tick more and more slowly, but will never reach the time that I see as I fall into the black hole. Notice that this is really an optical effect caused by the paths of the light rays."

I was thinking of the part two paragraphs down where they addressed your question about "we would not really see a black hole being invisible", pointing out that since light is not emitted continuously there will be a last photon emitted before the object crosses the horizon, and also that even continuous light would become so redshifted it'd be impossible to detect.

The part about it being an optical effect is troublesome. I assert that it is not an optical effect, as we have proven the time dilation effect of gravitational fields to be real and not just an optical illusion. (i.e. do the though experiment of a spaceship just skimming the gravitational field of a black hole would effectively travel to the future).

The only truly "objective" time dilation is when two clocks start at the same location, move apart, then reunite to compare time elapsed (proper time) locally. Any time you want to talk about the rate that spatially separated clocks are ticking relative to one another, this depends on your choice of coordinate system, and no coordinate systems are physically preferred in GR (although some are much more convenient). You seem to be thinking about what happens in Schwarzschild coordinates, where it takes an infinite coordinate time to reach the horizon, and the rate a falling clock is ticking approaches zero. However, in other coordinate systems on the same spacetime, like Eddington-Finkelstein coordinates or Kruskal-Szekeres coordinates (see some diagrams of the different coordinate systems here), the falling object crosses the horizon in finite coordinate time and it continues to tick at a nonzero rate all the way up until it hits the singularity.

 

[paulctan]

...You seem to be thinking about what happens in Schwarzschild coordinates, where it takes an infinite coordinate time to reach the horizon, and the rate a falling clock is ticking approaches zero. However, in other coordinate systems on the same spacetime, like Eddington-Finkelstein coordinates or Kruskal-Szekeres coordinates (see some diagrams of the different coordinate systems here), the falling object crosses the horizon in finite coordinate time and it continues to tick at a nonzero rate all the way up until it hits the singularity.

I agree that to the falling object, time passes normally and the object does indeed pass through the event horizon in a different time coordinate system.

However, my point is that to the outside universe the object never passes through the event horizon, so all the math and physics problems that come up in dealing with infinities and singularities never really happen in the outside universe. Is that a valid statement or am I missing something?? (Even if you argue that the outside universe sees only the last photon massively redshifted, at that point, it would have taken nearly infinite time to see that, so for all practical purposes, the object is stuck at the event horizon -- so doesn't that mean that stellar matter in a collapsing star will be stuck at the event horizon??)

Thanks for taking the time to enlighten me...

Paul Tan.

 

[JesseM]

I agree that to the falling object, time passes normally and the object does indeed pass through the event horizon in a different time coordinate system.

However, my point is that to the outside universe the object never passes through the event horizon, so all the math and physics problems that come up in dealing with infinities and singularities never really happen in the outside universe.

It's true that no event inside the horizon can have a causal effect on anyone outside it--that's the very definition of an "event horizon"! But then it's also true that there are regions of space sufficiently distant from us that nothing that happened there can have any causal effect on us because there hasn't been enough time since the Big Bang for light to cross the distance, and depending on the future expansion rate of the universe it may be that events from distant regions will never be able to have a causal effect on us because the space between us is expanding faster than light can cross the gap. In both cases it would be rather strange to conclude that these regions of spacetime don't exist, though.

Is that a valid statement or am I missing something?? (Even if you argue that the outside universe sees only the last photon massively redshifted, at that point, it would have taken nearly infinite time to see that, so for all practical purposes, the object is stuck at the event horizon -- so doesn't that mean that stellar matter in a collapsing star will be stuck at the event horizon??)

The FAQ article said it wouldn't actually take all that much time for us to receive the last photon from an infalling object (I'd guess the author did some calculations, or had seen them done by someone else):

Light from them is redshifted and dimmed, and if one considers that light is actually made up of discrete photons, the time of escape of the last photon is actually finite, and not very large. So things would wink out as they got close, including the dying star, and the name "black hole" is justified.