I What problems would 'black holes' not being formed solve?

[DrStupid]

My mistake: the Opening/Original Poster introduced the idea in post #27, not in post #1.

I don't even see it in #27. I read it the same way as zonde. The OP does not assume the existence of a singularity. He concludes that it does not exists because it never forms due to an ever increasing but finit time delation. This argumentation is at least valid for an external observer. And I expect it to be even valid for an observer in the center when Hawking radiation comes into play.

 

[russ_watters]

I don't even see it in #27. I read it the same way as zonde. The OP does not assume the existence of a singularity. He concludes that it does not exists because it never forms due to an ever increasing but finit time delation.

I'm not seeing a difference. You can call it "ever increasing but finite", but it "approaches infinity" and the existence of the asymptote is one of the features of that math. It's like saying for y=1/x as x approaches 0, y "approaches infinity" but remains finite. Even if you don't state the existence of the asymptote it is still there, as a feature of the math used in the argument.

And I don't understand why you and apparently zobd think this is an issue: we're not claiming the description is mathematically wrong, however you want to word it!

[edit] Btw, maybe what you really should want to know is why, if the scenarios are similar, did I introduce a slight alteration? I did it because it is cleaner. The changes in the arrangement of matter and simultaneous changes in the shape of the gravitational field are complex and I doubt have even been well modeled. So I think it is easier to visualize a static gravitational field and an object dropping into it. It's the same logic/question applied to a simplified problem.

[edit2] Acually, I would think the moment of creation requires quantum mechanics and general relativity: you'd have to describe something like the gravitational field around two neutrons that collapse into each other and form a tiny black hole. After that, everything else is the scenario I describe(with the addition of a non negligible growth rate).

 

[DrStupid]

It's like saying for y=1/x as x approaches 0, y "approaches infinity" but remains finite.

Exactly. And that's something completely different than y=1/x with x=0. Or do you really think that there is no difference between x=0 and x<>0?

 

[russ_watters]

Exactly. And that's something completely different than y=1/x with x=0. Or do you really think that there is no difference between x=0 and x<>0?

I'm saying that the equation describes both, whether someone mentions both or not. And again I ask: why are we splitting this hair?

 

[DrStupid]

And again I ask: why are we splitting this hair?

Because that's the topic. The argumentation of the OP means in your analogy above, that x will never reach the singularity x=0.

 

[russ_watters]

Because that's the topic. The argumentation of the OP means in your analogy above, that x will never reach the singularity x=0.

That's not an answer to my question. I'm asking what relevant difference there is that makes one description useful and the other not.

It's like we're discussing the speed of a pink racecar and you are arguing that it is salmon, not pink. So what? What does that have to do with the issue being discussed?

 

[Dale]

OP does not say or suggest that he considers infinite time dilation as absurd. He said that ever increasing finite time dilation

That is infinite. Infinite means that if you pick any finite number, it gets bigger.

You can not justify faulty argument by constructing a "straw man".

I don’t think that I am. I think that you are misunderstanding the OP’s argument.

 

[Dale]

These are two related but distinct things: existence of event horizon and formation of event horizon.

But the specific “absurdum” argued applies equally to both. The argued “absurdum” is infinite time dilation which occurs just outside the event horizon regardless of whether you are talking about Schwarzschild or OS.

 

[zonde]

But the specific “absurdum” argued applies equally to both. The argued “absurdum” is infinite time dilation which occurs just outside the event horizon regardless of whether you are talking about Schwarzschild or OS.

In Schwarzschild solution infinite time dilation occurs at finite proper time of infalling particle. It is not obvious that by analogy adopting proper time of particle at the center of collapsing body would be a good strategy in case of OS solution. Say distant observer is observing two different massive bodies shortly before gravitational collapse that have different gravitational time dilation at the center of the body. There is no reason to prefer time at the center of one body over the time at the center of the other body. But if we would try to adopt coordinate chart where each center of the body runs at it's own proper time we would accumulate time difference over time (for static bodies). So the obvious choice for distant observer is to keep his own time for coordinate chart. But in that chart infinite time dilation for collapsing body would be reached at infinite future of this coordinate chart or in plain English - never.
Alternatively you could try to adopt simultaneity that depends on dynamics of collapsing body. But this is highly non-trivial and besides it might lead to break point in simultaneity planes at the center of the body. If you try to avoid that it becomes even less trivial.

So the point is that analogy between Schwarzschild and OS regarding infinite time dilation is far from obvious.

 

[zonde]

I would like to add that from my previous post it seems that conclusion about physical situation might depend on the size of adopted coordinate chart. This situation is known by more than 2000 years from the time when Zeno came up with Achilles and the tortoise paradox. However philosophers have not reached consensus how the paradox should be solved.
My position is that the right resolution to the paradox is given by Diogenes i.e. (the reasoning of Zeno is sound but) it contradicts observations. It is sort of the thing that in science is taken as obvious: not every correct mathematical model describes reality and therefore we have to test our models against observations.

 

[DrStupid]

I'm asking what relevant difference there is that makes one description useful and the other not.

The difference is no singularity in one description and a singularity in the other.

 

[DrStupid]

That is infinite. Infinite means that if you pick any finite number, it gets bigger.

That just means that the limit is infinite but not the numbers and we are talking about the numbers.

 

[Dale]

That just means that the limit is infinite but not the numbers and we are talking about the numbers.

There is no infinite number. Infinite is inherently a limit.

 

[DrStupid]

There is no infinite number. Infinite is inherently a limit.

If you know that, why do you claim, that an "ever increasing finite time dilation" "is ifinite"? It always remains finite and defined. And no matter how big the number is, almost all positive numbers are bigger.

 

[Dale]

It is not obvious that by analogy adopting proper time of particle at the center of collapsing body would be a good strategy in case of OS solution.

I agree, so I would not pick that point. I would stay away from the center because that is where the singularity is and we expect our models to break down there. So pick another point where we expect the model to work, and all I said above applies.

We also do not pick the center of the Schwarzschild solution, so I was not even considering picking the center of the OS solution.

But in that chart infinite time dilation for collapsing body would be reached at infinite future of this coordinate chart or in plain English - never.

Yes, this is understood. Hence the OP’s “absurdum” and then the rebuttal follows validly pointing out that the observer’s coordinate chart doesn’t change the local physics at all.

So the point is that analogy between Schwarzschild and OS regarding infinite time dilation is far from obvious.

That is only because you are choosing a bad point to examine. Outside the singularity at the center the analogy is good. I was considering a point away from the singularity.

I think that is the source of our disagreement.

 

[Dale]

If you know that, why do you claim, that an "ever increasing finite time dilation" "is ifinite"? It always remains finite and defined.

That isn’t my wording, it is the OP’s. The OP’s wording is poor, but he is clearly (sloppily) referring to the infinite time dilation in the limit as you approach the event horizon. If you want to make an issue of his wording then take it up with him, not me. I won’t defend his wording, but I also don’t think it is worth correcting.

 

[Dale]

I would like to add that from my previous post it seems that conclusion about physical situation might depend on the size of adopted coordinate chart.

The physical situation does not depend on the coordinate chart at all. That is the whole point of writing physics in terms of tensors.

However philosophers have not reached consensus how the paradox should be solved.

This isn’t a philosophy forum. However, this statement does shed light on why you have been posting as you have. Zeno’s Paradox is considered resolved in the scientific literature, don’t waste our time here please.

 

[DrStupid]

That isn’t my wording, it is the OP’s.

"That is infinite." actually is your wording (see #67).

and with "This" you refer to

"OP does not say or suggest that he considers infinite time dilation as absurd. He said that ever increasing finite time dilation"

which is the wording of zonde and not the OP (again see #67).

The OP’s wording is poor, but he is clearly (sloppily) referring to the infinite time dilation in the limit as you approach the event horizon.

No he doesn't. He clearly assumes that this singularity will never be reached. That is equivalent to an always finite time dilation. If you do not see that, than you are actually missing the basic point of his idea.

 

[Dale]

which is the wording of zonde and not the OP (again see #67).

Oops, Yes you are right. The OP actually said infinite time dilation in post 27, so in context @zonde was discussing infinite time dilation which I understood. So if you want to take issue with the wording then do so with him, not me or the OP.

No he doesn't. He clearly assumes that this singularity will never be reached. That is equivalent to an always finite time dilation. If you do not see that, than you are actually missing the basic point of his idea.

Read his post 27. He is clearly objecting to the infinite time dilation. He considers infinite time dilation to be absurd so he is making an argumentum ad absurdum argument against the formation of the horizon. I am not missing his point at all, I understand both his point and also the argument he is using to support his point. I am defending the correct rebuttal of his argument.

 

[DrStupid]

So the obvious choice for distant observer is to keep his own time for coordinate chart.

How about setting the observer in the center and check if he will see the singularity formig before the black hole evaporates or not?

 

[Dale]

Does anyone know the metric for the interior portion of the OS spacetime? Also, the coordinates of the event horizon in the interior portion?

 

[DrStupid]

Read his post 27. He is clearly objecting to the infinite time dilation.

No, he doesn't. In #27 he says that he "don't see how time dilation could ever reach infinity at any point" and that the "the process would slow down, and prevent infinite time dilation occurring and hence a singularity" (highlighting by me). Please stop turning his argumentation into the opposite.

 

[Dale]

"don't see how time dilation could ever reach infinity at any point"

Yes. Argumentum ad absurdum.

Please stop turning his argumentation into the opposite.

I am not. That is how argumentum ad absurdum works.

 

[DrStupid]

Oh, sorry. I should have check before, what "objecting" actually means. Just forget my last post.

 

[zonde]

I agree, so I would not pick that point. I would stay away from the center because that is where the singularity is and we expect our models to break down there. So pick another point where we expect the model to work, and all I said above applies.

We also do not pick the center of the Schwarzschild solution, so I was not even considering picking the center of the OS solution.

But singularity is not there from the start. Say look at this picture (taken from https://arxiv.org/abs/1201.3660):

At first there is event horizon and only later singularity appears. In any case there is no singularity at the center of ordinary gravitating body. And it makes sense to pick the center as matter at rest at the center is not falling anywhere.

 

[zonde]

The physical situation does not depend on the coordinate chart at all. That is the whole point of writing physics in terms of tensors.

Do you mean that predictions of our models do not depend on chosen coordinate chart? Because obviously physical situation (reality) does not depend even from our models of physical situation, whether they are more or less correct or rather totally flawed.

But then maybe we are splitting hairs. If predictions are totally the same whether we describe collapsed stars as black holes or frozen stars, who cares what actually they are.

 

[Dale]

Do you mean that predictions of our models do not depend on chosen coordinate chart?

Yes, that is a better way to say it.

If predictions are totally the same whether we describe collapsed stars as black holes or frozen stars, who cares what actually they are.

I don’t think the predictions of black holes or frozen stars are the same. I think a black hole described with one set of coordinates is the same as a black hole described with another set of coordinates.

This is addressing your comment that our conclusions about the physical situation depend on the size of the coordinate chart. I think that is wrong, and you don’t change a black hole into a frozen star simply by changing the size of the coordinate chart.

 

[Dale]

But singularity is not there from the start. Say look at this picture (taken from https://arxiv.org/abs/1201.3660):
View attachment 229237
At first there is event horizon and only later singularity appears. In any case there is no singularity at the center of ordinary gravitating body. And it makes sense to pick the center as matter at rest at the center is not falling anywhere.

Ok, so this is a good picture to use. The event horizon has two sections. One section is the cylinder with straight edges going up off the top of the page, and the other section is a kind of round cap on the end of the cylinder.

The OPs objection was to infinite time dilation. I know that infinite time dilation occurs for the cylinder portion of the EH, but I don’t know if it occurs for the round cap section. So my comments above were discussing that section since it is the only section where I am sure that the OP’s argument arises.

 

[Zedertie Dessen]

We already discussed that above, it has already been resolved for some time now. As far as I know there is no current problem which would be resolved.

Thanks, but I don't see the paradox mentioned in this thread prior to my post. Could you point our where?
Also, I see several proposed resolutions to the black hole information paradox, but nothing saying it's definitely been resolved. Which solution do you mean?

https://en.wikipedia.org/wiki/Black_hole_information_paradox

 

[Dale]

Could you point our where?

Posts 1, 33, 35, 37.