Being at the position of a singularity before it is formed

[PeterDonis]

So if I understand you well you say that they are both a solution for the same problem

No, that's not what I said. I said they are both solutions to the same equation, the Einstein Field Equation. But they are not solutions to "the same problem", because the "problem" includes initial conditions as well as the equation.

why are we talking then about white holes at all in this topic

Because you described an alternative scenario which, though you didn't realize it, is a white hole instead of a black hole.

 

[PeterDonis]

cloud that is only expanding very slightly would eventually contract again, I suspect

There is an idealized mathematical solution of this form, which involves a white hole expanding into a dust cloud that is momentarily at rest at some finite size, and then the cloud collapsing into a black hole. This is equivalent to a finite portion of a spherically symmetric closed universe that expands and then recollapses, surrounded by spherically symmetric empty space.

 

[HansH]

But a white hole, the time reverse of that scenario, does not seem physically reasonable, because it would require that the initial singularity inside the white hole and white hole's horizon were already "built in" to the universe from the very beginning, and we don't know of any reason why that should be the case.

I still don't understand your statement that I described an alternative scenario which, though I didn't realize it, is a white hole instead of a black hole, because above you say that the initial singularity inside the white hole and white hole's horizon were already "built in" so how can that be build in when I start with a large cloud of dust with full vacuum outside that cloud? that seems to reverse cause and result ?

 

[Ibix]

because above you say that the initial singularity inside the white hole and white hole's horizon were already "built in" so how can that be build in when I start with a large cloud of dust with full vacuum outside that cloud?

You may choose to start at that point, but we can use Einstein's equations to determine both how the universe got there and where it will go. The answers depend on the velocity distribution of the matter, which you didn't specify clearly, which has led us to several different interpretations of what you meant.

Depending on what velocity distribution you pick, you may imply a universe with an infinite past in which the gas cloud has always been shrinking and will eventually collapse into a black hole. Or you may imply a white hole in the past and eternal expansiom in the future. Or a white hole in the past and a black hole in the future.

 

[PeterDonis]

how can that be build in when I start with a large cloud of dust with full vacuum outside that cloud?

Because it turns out, when you actually solve the Einstein Field Equation, that "large cloud of expanding dust with full vacuum outside that cloud" is not a complete specification of the initial conditions. There must also be a white hole horizon and initial singularity present at the start. This is just the time reverse of the fact that if you specify "large cloud of collapsing dust with full vacuum outside that cloud", you end up with a black hole horizon and a final singularity.

 

[HansH]

Because it turns out, when you actually solve the Einstein Field Equation, that "large cloud of expanding dust with full vacuum outside that cloud" is not a complete specification of the initial conditions. There must also be a white hole horizon and initial singularity present at the start. This is just the time reverse of the fact that if you specify "large cloud of collapsing dust with full vacuum outside that cloud", you end up with a black hole horizon and a final singularity.

I was not talking about a large cloud of expanding dust but just a cloud of dust not expanding or contracting so just put there. not sure if that makes any difference.

 

[Ibix]

I was not talking about a large cloud of expanding dust but just a cloud of dust not expanding or contracting so just put there. not sure if that makes any difference.

That's one of the spacetimes that has a white hole in the past and eventually collapses again into a black hole.

 

[HansH]

That's one of the spacetimes that has a white hole in the past and eventually collapses again into a black hole.

I think I understand your reasoning. You start with an initial situation in the past while I did not bother about the past and started 'now' by simply creating the situation building it up as is with a cloud of dust while the white hole did not exist anymore?

 

[PeterDonis]

I was not talking about a large cloud of expanding dust but just a cloud of dust not expanding or contracting so just put there.

Such a cloud is not stable. It will collapse in the future, and it could not have just been "put there" in the past, it must have been expanding in the past in order to have just reached momentary rest now.

In the usual Oppenheimer-Snyder model of the collapse of a massive star to a black hole, the star is assumed to have been stable in the past because it was not dust, it had enough pressure in the past to support it against gravity, the pressure being due to its high temperature as a result of fusion reactions in its core. When the fusion reactions stop, the pressure declines sharply, and Oppenheimer and Snyder idealized this as the pressure going to zero at some instant of time, after which the star would collapse as if it were a cloud of dust.

However, if the cloud of dust is assumed to be dust for all time, i.e., zero pressure for all time, then what I said in the first paragraph above applies.

 

[PeterDonis]

I did not bother about the past and started 'now'

But that still has implications for the past as well as the future, because GR is a deterministic theory, so specifying conditions at any time is sufficient to determine a complete solution.

 

[Ibix]

But that still has implications for the past as well as the future, because GR is a deterministic theory, so specifying conditions at any time is sufficient to determine a complete solution.

@HansH - you are free to ignore the implications your setup has about the past of your universe. However, one of the reasons GR is a difficult theory is that it's remarkably resistant to efforts to just wish things into convenient states, and sometimes ignoring how you got there can come back and bite you.

For example, in Newtonian gravity you can define a point mass and have it existing for ever, no problem. Attempting to do the same in general relativity gives you the Schwarzschild solution which, on a careful analysis, contains a black hole with a singularity, a white hole with another singularity, two separate exterior regions, a wormhole linking all four regions, and nothing but vacuum anywhere. Mostly we can just ignore all the complexity, but if you ask a question like "what would an observer who falls into a black hole see" you need to be aware of it. If you try to answer on the basis of a Schwarzschild black hole the answer is that you can see into that other exterior region, but that only exists because the Schwarzschild black hole is an unrealistic model. To answer the question for a black hole that formed from stellar collapse you'd have to look at an Oppenheimer-Snyder black hole, and you would need to be aware of the limitations of that model too - notably the lack of rotation, which might have effects.

In short, GR is a complicated theory and modelling apparently simple situations can lead to surprisingly wacky implications. There's nothing wrong with simple models, but you do need to be aware that things you think you can idealise away you sometimes can't, and that the idealisations you can make may lead to surprisingly complex phenomena lurking at the edges of your model, phenomena that may limit what you can do with the model.

 

[PeterDonis]

If you try to answer on the basis of a Schwarzschild black hole the answer is that you can see into that other exterior region

To be clear, you can only see the other exterior region if you fall into the black hole. You can't see either exterior region from the other exterior region.

 

[PeterDonis]

To answer the question for a black hole that formed from stellar collapse you'd have to look at an Oppenheimer-Snyder black hole

Note that in this model there is no second exterior region and no white hole.

and you would need to be aware of the limitations of that model too - notably the lack of rotation, which might have effects.

Not just the lack of rotation but the lack of pressure, which means there is no possibility of forming shock waves, heating up the infalling material so it emits radiation or outgasses, etc. Many physicists thought for several decades after the O-S model was proposed that these idealizations made it completely unrealistic as a description of an actual collapse. However, we now know from numerical simulations that the key features of the O-S model, the unavoidable formation of an event horizon and a singularity, are still present in more realistic models where exact spherical symmetry is not present and there is nonzero pressure so that all of those other things can happen.

 

[HansH]

Attempting to do the same in general relativity gives you the Schwarzschild solution which, on a careful analysis, contains a black hole with a singularity, a white hole with another singularity, two separate exterior regions, a wormhole linking all four regions, and nothing but vacuum anywhere. Mostly we can just ignore all the complexity, but if you ask a question like "what would an observer who falls into a black hole see" you need to be aware of it. If you try to answer on the basis of a Schwarzschild black hole the answer is that you can see into that other exterior region, but that only exists because the Schwarzschild black hole is an unrealistic model. To answer the question for a black hole that formed from stellar collapse you'd have to look at an Oppenheimer-Snyder black hole, and you would need to be aware of the limitations of that model too - notably the lack of rotation, which might have effects.

In short, GR is a complicated theory and modelling apparently simple situations can lead to surprisingly wacky implications. There's nothing wrong with simple models, but you do need to be aware that things you think you can idealise away you sometimes can't, and that the idealisations you can make may lead to surprisingly complex phenomena lurking at the edges of your model, phenomena that may limit what you can do with the model.

@HansH - you are free to ignore the implications your setup has about the past of your universe. However, one of the reasons GR is a difficult theory is that it's remarkably resistant to efforts to just wish things into convenient states, and sometimes ignoring how you got there can come back and bite you.

I think I understand what you mean: some situations are not possible because there is no possible past to get there.

 

[Ibix]

I think I understand what you mean: some situations are not possible because there is no possible past to get there.

Yes. Or just that the past (or some other corner of spacetime) that you need is a lot weirder than you might guess, and such weirdness can impose limits on the usefulness of the model.