I Being at the position of a singularity before it is formed

[PeterDonis]

I am basically looking for a proper criterion to be able to determine when in such theoretical situation a black hole forms.

A black hole forms from the gravitational collapse of an isolated object like a star. Strictly speaking, stars in our universe are not completely isolated, since there is still other matter in the rest of the universe. But if you think of what a star is like, it's a finite region of continuous matter surrounded by empty space, not extending out forever but at least extending out to a distance many times the star's own size (and many more times the Schwarzschild radius corresponding to the star's mass, which will be the size of a black hole formed from the star).

That is the key property that our universe does not have. If you talk about some large region of our universe, hundreds of millions of light-years across, it is not a single finite region of continuous matter surrounded by empty space. It is lots of matter scattered all through the region, with an average density that is roughly constant throughout the region, and with the same kind of distribution matter outside as inside. So it is not correct to think of any region of our universe as a whole as an isolated finite region of matter surrounded by empty space.

 

[PeterDonis]

The minimal mass of a neutron star is 1.4.

This is not correct. It's correct that the maximal mass of a white dwarf is 1.4 solar masses, so anything larger than that must be either a neutron star or a black hole. But that does not mean neutron stars smaller than that mass cannot exist. They can. They're just much less likely to form because the collapse process of a star that small can stop at the white dwarf stage.

 

[Hornbein]

This is not correct. It's correct that the maximal mass of a white dwarf is 1.4 solar masses, so anything larger than that must be either a neutron star or a black hole. But that does not mean neutron stars smaller than that mass cannot exist. They can. They're just much less likely to form because the collapse process of a star that small can stop at the white dwarf stage.

Right you are. The lightest neutron star so far seems to be 0.77. https://www.researchgate.net/publication/359752835_A_strangely_light_neutron_star

 

[HansH]

This is not true of our universe; there is no way to draw a sphere around any region occupied by mass in our universe and have all the mass inside and no mass outside. So the reasoning you are trying to use simply cannot be applied to our universe.

I know. This is pure a theoretical situation I created in order to better understand if a black hole could form based on a large cloud of (on average) low density material if all mass is within its own Schwarzschild radius.
In theory you could move all mass to another place and create this situation I assume?

 

[HansH]

This is not correct. It's correct that the maximal mass of a white dwarf is 1.4 solar masses, so anything larger than that must be either a neutron star or a black hole. But that does not mean neutron stars smaller than that mass cannot exist. They can. They're just much less likely to form because the collapse process of a star that small can stop at the white dwarf stage.

This situation triggered me to think of another theoretical situation. Suppose there would be another mechanism in nature that generates a very large repelling force at a much closer distance than occurs in a neutron star such that for larger mass than the maximum mass of a neutron star the mass further collapses and an event horizon forms, but within this event horizon while furter collapsing at a certain point this repelling force prevent further collapse. Then I assume you still see a black hole from outside but the formation of a singularity is then prevented. Would this be possble? or does the formation of an event horizon per definition mean that we get a singularity even if such a repelling force would be there? or is this the situation we think could occur due to quantum effects but we do not have a theory for yet and cannot define an experiment to test?

 

[PeterDonis]

This is pure a theoretical situation I created in order to better understand if a black hole could form based on a large cloud of (on average) low density material if all mass is within its own Schwarzschild radius.

Yes, that was the original theoretical situation you posed in the OP of this thread. But you have also asked about our universe as a whole, and our universe as a whole is a different situation, to which the theoretical model you posed in the OP of this thread is not applicable. So if you want to limit discussion in this thread to the theoretical situation you posed in the OP of this thread, which is a very good idea, you need to understand that discussion of our universe as a whole is not covered by that and would need to be done in a separate thread.

In theory you could move all mass to another place and create this situation I assume?

You can't just magically "move all mass to another place". You simply have two different theoretical situations: the one you posed in the OP of this thread, an isolated collapse, and the one that applies to the universe as a whole. They're different. That's all there is to it.

Suppose there would be another mechanism in nature that generates a very large repelling force at a much closer distance than occurs in a neutron star such that for larger mass than the maximum mass of a neutron star the mass further collapses and an event horizon forms, but within this event horizon while furter collapsing at a certain point this repelling force prevent further collapse.

This is not possible. Inside the event horizon collapse cannot be prevented by any means whatever; preventing the collapse would mean matter moving faster than light.

There are speculations connected with quantum effects that might generate the kind of "very large repelling force" you describe, but all of these effects would not just prevent a singularity from forming, they would prevent an event horizon from forming.

 

[Ibix]

This is not quite true. Our universe did not start out as a white hole. A white hole is an isolated region surrounded by empty space, just like a black hole. Our universe is not like that.

Yes. The thread of conversation to which I was responding seemed to me to be considering transplanting a large but finite region of our universe into an otherwise empty spacetime, then asking if it would be a black hole. That's a time reverse of an Oppenheimer-Snyder black hole, so a white hole.

I agree that a plain old FLRW universe did not start as a white hole.

 

[HansH]

transplanting a large but finite region of our universe into an otherwise empty spacetime, then asking if it would be a black hole. That's a time reverse of an Oppenheimer-Snyder black hole, so a white hole.

This I cannot follow. I would assume matter particles in this large region would attract each other, while in a white hole things repell each other. so I am lost here.

 

[PeroK]

I would assume matter particles in this large region would attract each other, while in a white hole things repell each other.

That makes no sense.

so I am lost here.

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

 

[Ibix]

This I cannot follow. I would assume matter particles in this large region would attract each other, while in a white hole things repell each other. so I am lost here.

No, in a white hole gravity is still attractive. Matter slows down as it comes out instead of speeding up as it falls in.

If your next question is "then why can't you enter a white hole" the answer is because of the way spacetime is curved. This is far past the point that you can try to understand general relativistic gravity as if it were just a few tweaks to Newtonian gravity. There are rough analogues to black holes in Newtonian gravity (although a close inspection shows that Newtonian "black stars" are very different from black holes and not entirely consistent), but there's nothing like a white hole.

 

[PeterDonis]

in a white hole things repell each other

No, they don't. Gravity is attractive in a white hole. In the scenario @Ibix is describing, which is the time reverse of the Oppenheimer-Snyder collapse in which collapsing matter accelerates as it collapses due to attractive gravity, expanding matter decelerates as it expands due to attractive gravity.

 

[HansH]

Yes I understand that part now: gravity remains attractive so things do not repell each other but could be the way spacetime is curved making it impossible for things to come closer as spacetime is 'flowing outwards'.
But then my next question would be: Why it is curved in this way in the example mentioned. If I compare it to the cloud of more dense iron particles in the openings message I thought we agreed it would form a black hole right and not a white hole? so what is it that makes it a black hole or a white hole? it that the scale of volume and density ?

 

[PeterDonis]

what is it that makes it a black hole or a white hole?

Whether stuff is falling into it or coming out of it. A white hole is the time reverse of a black hole.

Note that, unlike with black holes, we have no reason to believe that white holes actually exist in our universe. They're just a theoretical model; they're what you get when you take the time reverse of a collapse to a black hole such as you described in the OP of this thread.

 

[HansH]

Whether stuff is falling into it or coming out of it. A white hole is the time reverse of a black hole.

yes that I understand, but what causes it to be a black or white hole. so not the effect what happens but the reason why?

 

[PeterDonis]

what causes it to be a black or white hole

This question doesn't make sense. The terms "black hole" and "white hole" are just descriptions of particular solutions to the applicable laws of physics, in this case the Einstein Field Equation, that are time reverses of each other. (Because the Einstein Field Equation is time symmetric, the time reverse of any solution is also a solution.) It makes no sense to ask what causes a particular solution of the laws to be a solution; it's just math.

If you want to know why, for example, black holes are believed to actually exist but white holes are not, that's because the kind of scenario you describe in the OP of this thread, where a massive object like a star collapses to a black hole, seems physically reasonable; we already know that massive stars exist and that when they run out of nuclear fuel they will collapse. 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.

 

[PeterDonis]

what causes it to be a black or white hole

You seem to have the idea that there are physical systems out there that could possibly become either black holes or white holes, and you want to know what makes a given system become one or the other. That's not the case. Black holes, as I said in my previous post, are reasonable end points of a massive object like a star collapsing. White holes aren't reasonable end points for any physical process we know of.

 

[HansH]

The terms "black hole" and "white hole" are just descriptions of particular solutions to the applicable laws of physics, in this case the Einstein Field Equation, that are time reverses of each other. (Because the Einstein Field Equation is time symmetric, the time reverse of any solution is also a solution.)

So if I understand you well you say that they are both a solution for the same problem, but that in reality we think that only the black hole can exsist. So why are we talking then about white holes at all in this topic if we assume this is not a solution that occurs in reality. Or do I still miss something?

 

[PeroK]

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

That is a good question!

 

[HansH]

What you are describing is exactly the time-reversal of the Oppenheimer-Snyder black hole model. Oppenheimer-Snyder is a simple model of a stellar collapse into a black hole that is literally a spherical region of collapsing FLRW spacetime with vacuum outside. You've just replaced the collapsing region with an expanding region, so you are describing a white hole, which has an anti-horizon instead of an event horizon.

probably I was then put on the wrong leg by this answer where the white hole was mentioned for the first time in this topic. Therefore I already indicated that I did not understand why we talked about a white hole here and not a black hole.

 

[Ibix]

probably I was then put on the wrong leg by this answer where the white hole was mentioned for the first time in this topic.

The problem is that you didn't specify the conditions you were talking about clearly. What happens (and, indeed, what happened before) to a spherically symmetric patch of constant density matter surrounded by vacuum depends on the velocity distribution of the matter, among other things. You seemed to me to be talking about a matter distribution like our universe at the time, so I answered on the basis of a large but finite expanding cloud of galaxies. If you back track that, it comes from a white hole, and if you run it forwards it does not form a black hole (or at least, not necessarily - a cloud that is only expanding very slightly would eventually contract again, I suspect).

If, instead, you are interested in an initially static or contracting cloud then yes this would eventually form a black hole.

The key point is that it isn't just mass and density that defines what happens to something, but also the initial velocities (and in a more realistic model, things like pressure and other interactions like fusion).

 

[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.