Hollow spherical blackhole thought experiment

[Instine]

So do you agree with the images above? i.e. do you think there will only be one event horizon? And thereby a naked singularity in one or other universe?

 

[Instine]

I've had a think about your bubble JesseM. Do they run out of juice, these things? Or do they keep growing for ever?

 

[JesseM]

I've had a think about your bubble JesseM. Do they run out of juice, these things? Or do they keep growing for ever?

Not sure, but if it's expanding at the speed of light, it seems unlikely it would slow down. But if the universe keeps expanding, there should be regions of the universe it will never reach, because the distance between them and the edge of the bubble would be increasing at faster than the speed of light thanks to the expansion of space.

 

[Instine]

Which means you could be in a time and place traveling at a real velocity, and view the effects of the vacuum bubble without being annihilated.

 

[Instine]

I believe in a kind "fighting chance principle". i.e. yes galaxy destroying powers may exist (I believe they do), but they must be finite, not only in their probability of occurring, but also in their 'reach'. Otherwise we'd have no universe to see before us.

If all that happens in our TE is the shell implodes at the speed of light, FP's situation breaches this principle for me. But as you say, your bubble (if they exist) must have finite reach, or the universe must be infinitely old, or have been created infinitely large. Which it may have been.

 

[pervect]

Hmm, I would have thought there wouldn't be a very close analogy to the classical case, since nothing new or unusual happens when you introduce point masses of infinite density into Newtonian physics or point charges of infinite charge density into electromagnetism, but singularities in GR are associated with phenomena that you don't see in extended non-collapsing masses, namely event horizons and the termination of worldlines which hit the singularities.

Basically, I was suggesting that to find out if there is a black hole, you look for a "trapped null surface" - a region from which light can't escape.

Without a trapped null surface, you have no event horizon (and hence no black hole).

Unfortunately, while the presence of a trapped null surface proves that there must be a singularity by Penrose's theorem, the absence of a trapped null surface doesn't actually prove that there isn't a singularity if you want to get reallly technical.

So my argument doesn't really rule out a singularity, but it does rule out a black hole.

Suppose we had a 2D spherical surface in GR whose radius was larger than than the Schwarzschild radius for that mass--would it still have an event horizon near the surface (if not, would it be a form of 'naked singularity'?) and would wordlines hitting it still be terminated? What does this mean in the case of an extended mass whose radius is larger than the Schwarzschild radius and whose pressure keeps it from collapsing, like a star? I assume it'd only be identical to the Schwarzschild solution beyond its surface, but not inside it?

You should be able to see that there isn't any trapped null surface for a sphere of mass M and radius R such that r is larger than the Schwarzschild radius of M.

The spherical symmetry of the problem guarantees that there will be a spherically symmetrical solution.

The 'r' coordinate can be defined as a radial coordinate where scaled such that the a circle of that radius has a circumference of 2*Pi*r, or alternately, an area of 4*Pi*r^2. (r is not a distance from the center, but is a function of distance from the center.)

Birkhoff's theorem says that the metric is going to be -(1-2M/r) dt^2 + 1/(1-2M/r) dr^2 for r > R, where 2*Pi*R is the circumference of the sphere.

The metric will be -(1 - 2M/R) dt^2 + 1/(1-2M/R) dr^2 for r<=R

This is essentially what George said earlier.

To calculate the curvature tensor for the above metric you do have to comit the minor sin of allowing delta functions, otherwise you have to insist that the sphere is really very thin, rather than having zero thickness.

You can see by inspection that for R > 2M the metric is well behaved - it's the same metric outside the sphere for anybody of mass M and radius r>R, basically. And inside the sphere, it's just a Minkowski metric.

 

[chronon]

The way I'm now reading it, is we will have a naked singularity in at least one of the universes.

I think that you're using the word singularity in two different ways. Firstly the usual way, the singularity contained within the event horizon of a black hole. Secondly, the surface of finite mass but zero thinkness, which might be called 'singular' in some sense, but the consensus seems to be that this isn't a gravitational singularity. Certainly if you approached it from the outside you wouldn't notice any great problems. Suppose that the sphere has the same mass and radius as the earth. Then the gravity outside would be just the same as that on Earth - however close you approached the shell. As George points out, on the inside of the shell the gravitational force will be zero.

 

[Instine]

Re singular 2d mass/ singularity/singularity shell, I didn't realize there is a consensus on what to call them. Any ideas? In this case, will Singular Shell do?

As George points out, on the inside of the shell the gravitational force will be zero.

I'm aware of the flat space-time in the shell (read earlier post explaining the paradox).

Certainly if you approached it from the outside you wouldn't notice any great problems. Suppose that the sphere has the same mass and radius as the earth. Then the gravity outside would be just the same as that on Earth - however close you approached the shell.

This is another good point. So this would be the 'Thin Crust' (I'm hungry again).

It's true enough, but what if it where massive enough to have it's event horizon beyond the shell.

 

[JesseM]

I think that you're using the word singularity in two different ways. Firstly the usual way, the singularity contained within the event horizon of a black hole. Secondly, the surface of finite mass but zero thinkness, which might be called 'singular' in some sense, but the consensus seems to be that this isn't a gravitational singularity. Certainly if you approached it from the outside you wouldn't notice any great problems. Suppose that the sphere has the same mass and radius as the earth. Then the gravity outside would be just the same as that on Earth - however close you approached the shell. As George points out, on the inside of the shell the gravitational force will be zero.

George also said he thought tidal forces would become infinite on the surface itself, and he wasn't sure whether or not all worldlines would terminate when they intersected it. I suppose that whether or not you call it a "singularity" is just a matter of terminology though...I've been calling it a "singular surface" to try to avoid confusion. The focus of Instine's argument seems to be on the fact that the inside and outside of this surface would be absolutely cut off from each other, with no possibility of exchanging information, so it would be interesting to know whether this is in fact true. I already brought up the issue of an electromagnetic wave hitting the singular surface, I also wonder whether a gravitational wave hitting it from the outside could have any effect on the curvature of spacetime inside.

 

[JesseM]

It's true enough, but what if it where massive enough to have it's event horizon beyond the shell.

I think what people are saying is that there would only be an event horizon if the surface's radius was smaller than or equal to the Schwarzschild radius for its mass, otherwise there would be none.

 

[Instine]

Great, we're all agreed on something then

 

[Instine]

So for our r < Sr situation?

We all agree there's no field inside, but an event horrizon outside.

At this stage I'd love it if all of you guys could post a quick diagram of what you believe is going on at all significant radii.

(I feel like I'm setting home work )

Me? Well as you can tell, I don't know, and I don't think you can say, which is why I call it a paradox, but if anyone of you can give a cohesive model, I'd be delighted.

Again thanks to all of you

 

[chronon]

I guess in the case where the system forms a black hole the observer inside will go on experiencing 0G until he gets crushed by the infalling shell. So where's the singularity if it's not at the centre? Well since time and space get swapped around, for observers inside a black hole the singularity is not at the centre its in the future

 

[chronon]

George also said he thought tidal forces would become infinite on the surface itself

I wouldn't read too much into this. The tidal effect is due to the gravitational force changing with distance, and in this case there's no great change in the force ( from e.g. 1G outside the shell to 0G inside), it's just that the distance over which it changes is zero.

 

[Instine]

I thought we were now only conciderng the shell radius being greater than its Schwarzschild. Again, sorry to be bossy, but as OP author, I'd like to corral this back to the main issues of the thread.

We're considering a situation where there is an event horizon outside, and [non?] inside. Thickness of the shell is zero.

Is there a naked singular surface presented to FP? At the very least he seems to be able to veiw the effects of infinite tidal forces. I'm sure this will through up an issue or three.

Its still proving a head scratcher, no?

 

[Instine]

BTW, re the collaspse at the speed of light, why do people think this? What suggests c as the radial velocity of encroaching doom (supposing for a moment it isn't paradoxical)?

And I don't see any pictures yet. Come on you guys, don't be lazy, I want to see diagrams!

Blow the cobwebs off MS paint if you don't have photoshop.

 

[JesseM]

I wouldn't read too much into this. The tidal effect is due to the gravitational force changing with distance, and in this case there's no great change in the force ( from e.g. 1G outside the shell to 0G inside), it's just that the distance over which it changes is zero.

But are you saying nothing would happen to you if you hit the singular surface, you'd just pass right through it? George Jones wasn't sure about this...I wonder if general relativity gives clear-cut rules for when worldlines are terminated and when they aren't, or if you could model this situation either way and it would be a valid solution. I remember one of the problems with naked singularities is that they allow for multiple solutions without a way to choose between them, because it would be consistent for anything to pop out of one at any moment...the last paragraph of section 4.3.2 from this article says:

The most problematic kinds of singularities, in terms of determinism, are naked singularities (singularities not hidden behind an event horizon). When a singularity forms from gravitational collapse, the usual model of such a process involves the formation of an event horizon (i.e. a black hole). A universe with an ordinary black hole has a singularity, but as noted above, (outside the event horizon at least) nothing unpredictable happens as a result. A naked singularity, by contrast, has no such protective barrier. In much the way that anything can disappear by falling into an excised-region singularity, or appear out of a white hole (white holes themselves are, in fact, technically naked singularities), there is the worry that anything at all could pop out of a naked singularity, without warning (hence, violating determinism en passant). While most white hole models have Cauchy surfaces and are thus arguably deterministic, other naked singularity models lack this property. Physicists disturbed by the unpredictable potentialities of such singularities have worked to try to prove various cosmic censorship hypotheses that show -- under (hopefully) plausible physical assumptions -- that such things do not arise by stellar collapse in GTR (and hence are not liable to come into existence in our world). To date no very general and convincing forms of the hypothesis have been proven, so the prospects for determinism in GTR as a mathematical theory do not look terribly good.

So maybe something similar is going on with the singular surface when it has no event horizon, it might be equally consistent with GR for an object hitting it from one side to come out the other side as if it had just passed right through, or to disappear, or to reappear after a delay, etc. I'm just speculating obviously, I have no idea if the singular surface would really behave like a naked singularity in this sense.

 

[chronon]

But are you saying nothing would happen to you if you hit the singular surface, you'd just pass right through it? .

Yes, as far as gravity is concerned. Suppose that there was such a sphere made of dark matter, so that we didn't interact with it via any other forces. The my intuition is that we would be pulled towards it and go straight through the surface without being squashed or pulled apart or anything else particularly drastic.

 

[JesseM]

Yes, as far as gravity is concerned. Suppose that there was such a sphere made of dark matter, so that we didn't interact with it via any other forces. The my intuition is that we would be pulled towards it and go straight through the surface without being squashed or pulled apart or anything else particularly drastic.

Well, what about the naked singularity comparison? If a point particle's worldline hit a naked singularity, then since there'd be no event horizon do you think it would pass through it and continue on its merry way, or be absorbed into it? Again, I think the point about indeterminism in the presence of naked singularities may mean that either is possible, and a singular 2D surface with no event horizon could perhaps be considered a form of naked singularity.

 

[chronon]

Well, what about the naked singularity comparison? If a point particle's worldline hit a naked singularity, then since there'd be no event horizon do you think it would pass through it and continue on its merry way, or be absorbed into it? Again, I think the point about indeterminism in the presence of naked singularities may mean that either is possible, and a singular 2D surface with no event horizon could perhaps be considered a form of naked singularity.

The point about the naked singularity is that GR doesn't say what happens to the particle after it hits it, whereas my feeling is that the behaviour of a particle at the 2D surface would be perfectly deterministic - it would just go through it. But I can see that we're going to need some maths here to decide one way or the other.

 

[Instine]

Sorry Chronon but I think you're way off the mark here. If the radious of the singular shell is less the the schwarzchild radious, there will be an event horizon 'out side', This mean the same fate is meat by any incoming particle/observer, as with any black hole.

From inside, if FP were to reach his arm through, he would be feeling no gravitational froce, but his arm would feel infinite force (pushing back on him).

Such infinite properties can not be seen according to the Cosmic Censorship principle.

Why do you think that no harm will come to anyone falling in or attempting to get out? Remember we are now looking at a situation where the mass is great enough to create Sr bigger than r.

And where are the diagrams?

 

[JesseM]

Sorry Chronon but I think you're way off the mark here. If the radious of the singular shell is less the the schwarzchild radious, there will be an event horizon 'out side', This mean the same fate is meat by any incoming particle/observer, as with any black hole.

I understood us to be talking about the case where the radius was greater than the Schwarzschild radius, so there was no event horizon.

From inside, if FP were to reach his arm through, he would be feeling no gravitational froce, but his arm would feel infinite force (pushing back on him).

Interesting, I hadn't thought of the issue of what would happen to an object traveling outward in the case where the radius is less than the Schwarzschild radius. Intuitively it seems that either your description would be true (since I understand pervect's comment about Birkhoff's Theorem in post #82 to mean that inside the surface spacetime is flat, but outside it's just like the inside of a black hole, where nothing can move outwards even briefly), or else anything coming into contact with the surface would simply be annihilated instead of feeling an "infinite force".

Such infinite properties can not be seen according to the Cosmic Censorship principle.

But cosmic censorship is only a conjecture, the evidence that it actually holds is not all that strong. And in any case, once you're talking about what would be seen by an observer in the interior of the singular surface after the surface's radius has contracted to smaller than the Schwarzschild radius, cosmic censorship wouldn't apply to his observations any more than it would apply to the observations of someone inside a regular black hole, it is only supposed to apply to observers outside the event horizon.

Why do you think that no harm will come to anyone falling in or attempting to get out? Remember we are now looking at a situation where the mass is great enough to create Sr bigger than r.

Again, I think chronon was talking about the case where there was no event horizon--that's what I was talking about anyway.

And where are the diagrams?

How would a diagram be helpful here? You'd just have a circle representing the singular surface, and perhaps a larger one to represent the event horizon if the surface's radius was smaller than the Schwarzschild radius. That's pretty simple to visualize, and I don't know what else could go in the diagram.

 

[Instine]

But cosmic censorship is only a conjecture, the evidence that it actually holds is not all that strong. And in any case, once you're talking about what would be seen by an observer in the interior of the singular surface after the surface's radius has contracted to smaller than the Schwarzschild radius, cosmic censorship wouldn't apply to his observations any more than it would apply to the observations of someone inside a regular black hole, it is only supposed to apply to observers outside the event horizon.

FP is an observer! Poor fella that he is.

How would a diagram be helpful here? You'd just have a circle representing the singular surface, and perhaps a larger one to represent the event horizon if the surface's radius was smaller than the Schwarzschild radius. That's pretty simple to visualize, and I don't know what else could go in the diagram.

We may have avoided talking at cross purposes just now, but also, I was stupidly thinking there would be an event horizon inside the shell (for 9 years!) until I drew a diagram for you guys to explain what I was invisaging. Seriously diagrams help. They make easy mistakes a lot more obvious. I can't force you, its a forum, not boot camp, but I think it would help. You too Chronon et al. Please?

 

[JesseM]

But cosmic censorship is only a conjecture, the evidence that it actually holds is not all that strong. And in any case, once you're talking about what would be seen by an observer in the interior of the singular surface after the surface's radius has contracted to smaller than the Schwarzschild radius, cosmic censorship wouldn't apply to his observations any more than it would apply to the observations of someone inside a regular black hole, it is only supposed to apply to observers outside the event horizon.

FP is an observer! Poor fella that he is.

But as I said in the bolded section, the "cosmic censorship conjecture" is not meant to apply to all observers. It just says that all singularities must be "clothed" by an event horizon, so that observers outside the event horizon will not have any problems with the weird indeterministic properties of "unclothed" singularities. But observers inside the event horizon have no such luck. In an ordinary nonrotating black hole the singularity would always lie in the infalling observer's future until he hit it, but I don't think the same is true of rotating black holes (see this wikipedia article on the ring singularity, which should be taken with a grain of salt since it needs expert review), the ring singularity is something they could actually observe without colliding with it (in classical GR of course, quantum gravity would probably change things).

We may have avoided talking at cross purposes just now, but also, I was stupidly thinking there would be an event horizon inside the shell (for 9 years!) until I drew a diagram for you guys to explain what I was invisaging. Seriously diagrams help. They make easy mistakes a lot more obvious. I can't force you, its a forum, not boot camp, but I think it would help. You too Chronon et al. Please?

But was it really the diagram that helped, or just the realization that the spacetime inside the surface would have to be flat so there'd be no event horizon? If my diagram would just be a single circle representing the singular surface, or two concentric circles with the inner one as the surface and the outer one as the horizon, are you going to get anything out of this by seeing it drawn that you wouldn't from seeing that description?

 

[Instine]

I've known the spacetime would be flat for the 9 years I've been thinking about this. If your re-read the OP you'll see I've always been aware of that.

Although this is all highly improbable to the point of absurdity, its worth noting, that in theory the fool/hero would not be crushed by the gravitational field of the spherical black hole surrounding him (do the vector analysis if you like)

Its a major point of the thought experiment. Sorry if I'm no good at describing my thoughts. Yet I was stupid enough to think there had to be a 'thick' event horizon next to a point think mass. Not till I drew it, did this leap out as being silly. Seriously, drewing helps.

I'm going to kick it off with some scetches (In a bit, I'm 'busy').

Anyway. Re the former point, he is 'ouside' the hyper dense shell. If you see what I mean. He's outside, in as much as he can look upon its surface. He can't see the indeterministic properties any more than we can (I agree with the logic of cosmic censorship, though I note and understand your scepticism). Are such properties visible to him, and if they're not why not? There's no event horizon. Or is there...


This is the crux of the issue. Every time I try to model the inside, it bugs out. Even my original issue remains unsolved, in my eyes (though your 'probe' comment is concerning me re that). i.e. there isn't enough information withing the lesser universe to sustain the reallity of the barrier (which I erroneously referred to as the event horizon).

This naked hyper desity is now my biggest worry though.

 

[JesseM]

Its a major point of the thought experiment. Sorry if I'm no good at describing my thoughts. Yet I was stupid enough to think there had to be a 'thick' event horizon next to a point think mass. Not till I drew it, did this leap out as being silly. Seriously, drewing helps.

But again, would drawing a single circle or two concentric circles help in a way that my description of them does not?

Anyway. Re the former point, he is 'ouside' the hyper dense shell. If you see what I mean. He's outside, in as much as he can look upon its surface. He can't see the indeterministic properties any more than we can (I agree with the logic of cosmic censorship, though I note and understand your scepticism). Are such properties visible to him, and if they're not why not? There's no event horizon. Or is there...

All your arguments seem to be based on the tacit assumption that the laws of physics as seen by him can only take into account things which he is actually capable of measuring, but you've never really provided any reasons that we should accept this assumption. Isn't GR based on taking a sort of godlike "objective" point of view where we can see the whole of spacetime at once, even if no individual observer within spacetime has access to all this information? And from this godlike point of view, the observer within the singular surface is also within the event horizon that surrounds the singular surface, even if this horizon cannot be seen by him. As I understand it, "cosmic censorship" is supposed to be based on whether an observer really is within an event horizon or not, not whether or not he can know if he is. It seems like you're conflating epistemology with ontology, so to speak...maybe you could justify this in terms of the centrality of information in quantum mechanics or something like that, but your perspective at least needs to be argued for rather than just taken for granted.

there isn't enough information withing the lesser universe to sustain the reallity of the barrier (which I erroneously referred to as the event horizon).

That's the sort of thing I'm talking about. Who says "information" is needed to "sustain the reality" of anything in the first place? You haven't really addressed my analogy of the expanding bubble of true vacuum destroying the false vacuum...if there can be no information about the true-vacuum bubble in the false-vacuum region until the moment it hits you, then would you argue that there isn't enough information in the false-vacuum region to sustain the reality of the bubble, so being destroyed by such a bubble is something we can rule out a priori?

 

[Instine]

Darn. I may have just lost my battle to keep this off the philosophy forum.

..., but your perspective at least needs to be argued for rather than just taken for granted.

Of course your right enough here. So I'll give it a go, but it will be very philosophical (I hope the moderators can stand this hiatus):

With regards to the information, required to sustain a reality:

If we are to believe in a reality, it must be of real facts. Events that occur must be of real cause. It follows the that without real cause, there are no real events we can expect. Causality is all well and good, but what about the unexpected. The unexpected is always possible, but to progress in thought (as in life) we must always be optimistic and believe that we will not be overwhelmed by the unexpected. Else why try to predict anything? It may do us well to say, that we cannot assume the cosmic censorship principle to be fact. But assuming that it is false, does us no favours at all. Furthermore we can never disprove it, by its very nature. But we can assume it, knowingly running the risk that it may not be true. At worst case, it is a taughtology. Simply stated as, 'we can never observe that which we cannot observe', this becomes more apparent. One can also see the links with the anthropic principle (strong, in particular). And I can see your not convinced by this form of argument. So...

Put it this way, if no physics you know can predict what would actually be observed, you can be an optimist, or a pessimist. You must resort to game theory. Which guess must you assume, in order to make most likely the greatest pay off. Or the greatest mean payoff.

Take the following situation. There is a finite (but ridiculously small) chance that this form of event could envelope our visible universe, through some gargantuan event beyond our scale of perception. Should we worry that this may happen? knowing that we can't predict, prevent or even observe our impending doom? Or should we believe it is the least likely out come, but without factual reason. Like I say this is game theory not physics. Game theory says, if you have to play, this is how you should play it. And we have to play.

The cosmic censorship issue is very deductivist. As is the anthropic principle and my 'fighting chance' principle. If you're not convinced by deductivism, them I'm unlikely to convince you otherwise, but Popper may. You may remember I begrudgingly accept the use of the Dirac delta function. I do so because of this principle. It is not based in sound fact. Nor can it ever be observed to be so, but the alternative, is lots of our maths falls apart. It will be forever an unknown, but for now, I'll believe it as its the best chance of building on what we do know.

I was expecting to really go off into one there, but I've managed to put the breaks on. I'll let you pick up on/apart anything before I continue.

 

[pervect]

And where are the diagrams?

I've been meaning to get to this for a while. There are some diagrams at

http://casasrv.colorado.edu/~ajsh/collapse.html#collapse

There are of course, a lot of possible diagrams, it's not clear what you think you want a diagram of. My favorite diagram is

"Eddington-Finkelstein spacetime diagram of the collapsing sphere"

This shows the 'r' coordinate (circumference divided by 2Pi) of a collapsing sphere - this is, as the documentation says, the white line.

This coordinate is plotted against the Finklestein time coordinate. This time coordinate is time adjusted so that light moves at a constant coordinate velocity.

What you need to realize (and may not) is that different observers have different clocks, and different rulers, so no one diagram can show you what happens from all perspectives.

In the "Finklestein diagram", the red line shows the "absolute horizon" (there are a couple of different flavors for "the" horizon as I mentioned earlier), and the blue line shows the singularity that eventually arises when the sphere hits zero radius.

Various background "purple" lines are infalling light rays.

You'll note that Hamilton makes the same comments I made earlier about the metric inside the sphere being a FRW metric. This means that, as I mentioned earlier, the sphere gets smaller and smaller, shrinking uniformly, from the POV of someone on the sphere.

The geometry outside the sphere is the Schwarzschild geometry. The geometry inside the uniform sphere is, curiously enough, the same Friedmann-Robertson-Walker geometry that describes the expanding Universe, except that the `Universe' here is collapsing. The fact that the collapse started from zero velocity at infinity means that the interior geometry is flat, and the density of the sphere is the critical density.

You rather "blew this off", when I last mentioned it, IIRC. I'm afraid I can't really explain to you WHY this happens without math that you don't have. It's probably unfair to expect you to believe that this is what happens without a source. Well, now you have a source, and you might want to start to think about accepting that this is indeed what actually happens in a spherically symmetrical collapse, and that if you have ideas that contradict this that they are your own personal ideas that disagree with the accepted predictions of General Relativity.

What happens in a nutshell: you start out sitting on a sphere of finite size. A finite amount of time later (as measured by your watch) you (and the entire rest of the sphere) are compressed to a mathematical point - a singularity.

At the same time that I say this, I have to add in the cautions. Specifically, a real collapse would probably NOT be spherically symmetrical, and that in this toy example we have not included complicating factors like rotation at all. Nor have the effects of quantum gravity been factored in - many people think that quantum gravity will keep the central singularity of the BH from being a true mathematical point.

But I think that even this rather "idealized" spherically symmetric collapse is enough to show that whatever ideas you have been working on on your own for these last years are not the same ideas that arise in GR - i.e. that you are making predictions that are different from those predicted by GR, so that your theories cannot be the same as GR.

Speaking of sources, let me suggest that as a popular reference, that you check out Kip Thorne's book "Black Holes & Time Warps: Einstein's outrageous legacy".

This talks a lot about black holes (and some exotica like wormholes & time travel as well), is written on a popular level, and is by an acknowledged expert in the field.

 

[Instine]

There are of course, a lot of possible diagrams, it's not clear what you think you want a diagram of.

One of a sphere of no thickness but a mass that proscribes a Schwarzschild radius greater than the radius of the sphere. Then two images, one of the inside a small finite moment late, and one of the outside of the schwarzchild radius, a small moment later.

Rates of movement would get big browny points!

 

[Instine]

OK I've just finished reading your post pervec. I hate to say it again but I think youre still missing the point. You're still talking about a classical black-hole, forming by the usual means. We're discussing a shell. A shell that is highly improbable, but it seems, possible. No, this will not form via a normal collapse of a sphere. I didn't say it would. Only by a monstrous amount of crushing energy hitting a stationary sphere uniformly. I laughably suggested bombs on a moons surface. Sure enough that wouldn't come close, but this is a thought experiment. Einstein himself was very keen on them, you may know. He did not have Borh asking him where he'd get a long enough cable for his infinitly tall elevator shaft though. Do you see?

I know enough maths to understand the points you've raised, but they are not relevant. I thought we'd made that more clear by now. Again sorry if I'm confusing you.

You're right about time being relative, and unsurprisingly, I'm aware of this. However, what of severed timelines? what if there where a wall of infinite density between you and the rest of your previous universe? This is the question being asked.

I promise you, I did all the stuff your talking about in first year at Kings. (although I've apparently forgotten most of it). But you don't seem to have grasped that we're discussing a hypothetical here.

 

[Instine]

I've just finished reading my own post and it sounds horribly pompous. Sorry about that, its not how its meant.

 

[Instine]

Re-readng some of the earlier responses I see AlphaNumeric hit the nail right on the head, but I dismissed him out of hand! So firstly apologies to AlphNumeric!

Secondly, come back. If you can forgive me, it would be great if you could expand on what happens to FP.

 

[pervect]

OK I've just finished reading your post pervec. I hate to say it again but I think youre still missing the point. You're still talking about a classical black-hole, forming by the usual means. We're discussing a shell. A shell that is highly improbable, but it seems, possible. No, this will not form via a normal collapse of a sphere. I didn't say it would. Only by a monstrous amount of crushing energy hitting a stationary sphere uniformly. I laughably suggested bombs on a moons surface. Sure enough that wouldn't come close, but this is a thought experiment. Einstein himself was very keen on them, you may know. He did not have Borh asking him where he'd get a long enough cable for his infinitly tall elevator shaft though. Do you see?

I know enough maths to understand the points you've raised, but they are not relevant. I thought we'd made that more clear by now. Again sorry if I'm confusing you.

You're right about time being relative, and unsurprisingly, I'm aware of this. However, what of severed timelines? what if there where a wall of infinite density between you and the rest of your previous universe? This is the question being asked.

I promise you, I did all the stuff your talking about in first year at Kings. (although I've apparently forgotten most of it). But you don't seem to have grasped that we're discussing a hypothetical here.

It's definitely possible that there is some sort of communication problem and that I'm not understanding you, and vica-versa.

How much math do you have? Specifically, do you have enough that you can specify the stress energy tensor of the system you want to analyze?

If we can talk in terms of stress-energy tensors (and metrics), it will aid communication quite a bit.

I find that using the math takes quite a bit of effort on everyone's part, but it seems to be the only way to communicate in many cases. A lot of time philosophical differences get in the way of communicating about science.

Finally, on the broad overview level, my perception is that you are becoming isolated from the mainstream.

Why do I say this? Let's look at your usage of language.
"Information needed to sustain a reality".

What does this mean?

I assume, that as the result of your thinking "over the years", you actually do have something in mind and are trying to communicate it. I'm equally certain that I don't get it, and that it's not in the subset of modern GR physics books that I have on hand. Now maybe this remark could make sense viewed some other field with which I am not familiar (string theory, perhaps) - but without any references on your part (after having asked for them) it's hard to tell, and I basically have to assume that it's your own ideas here, not something from the literature. If it did turn out to be from the literature of string theory, for instance, it would be easy to suggest that you try the string theory forum and not the GR forum.

Thus in general terms, I would recommend reading everything and everything _mainstream_ that you can find on black holes, at whatever level you are comfortable with, in order to aid communication if nothing else. (When you use your own private language, you are going to get a lot of blank looks. If you can express yourself in mainstream concepts, you're a lot more likely to be able to get a response.)

My answer to being "away from the mainstream" is to do more mainstream reading, in brief.

I particularly like Kip Thorne's books, as I mentioned. Hamilton's webpage on black hole that I posted some references from isnt' bad either. There are a lot of "black hole FAQ's" out there that are pretty good, too (I could give a more complete list, but you can probably find them.)

I do suspect from what I've heard so far that you will find that your ideas are basically not the same as GR, though - don't be too terribly surprised if you find this to be the case.

 

[Instine]

OK, again, let's not waist time with this. If the moderator wants to close the thread because I don't give references to putive hypotheses in a discussion about a thought experiment, then so be it. Otherwise, I'm not wanting discuss how much maths I have. Metric Tensors strech me. But I have more maths than Einstein had when he penned SR.

No I don't want to talk in maths, its a thought experiment. As such, its rare that we will need more than 1, 0, oo and X as a finite value.

So - back to the actual question. If there is a spherical wall of infinite density surrounding you, what happens next? I'd didn't ask that anyone caluculate which forces of what magnitude would be felt where. but if you feel there is something to explore there, feel free.

There is little point in always discussing the orthodox in terms that have been used before. If you'd like references to this end:

"Imagination is more important than Knowledge", Albert Einstein

"Reading, after a certain age, diverts the mind too much from its creative pursuits. Any man who reads too much and uses his own brain too little falls into lazy habits of thinking. ", Albert Einstein

"As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality. ", Albert Einstein.

Yes I know, these are quotes, not references, but its worth noting that not a single refence was made in Einsteins first submition of SR.

As I've said before, Einstein was very fond of thought experiments, and not so, of maths. So let's indulge him, and me, and not get hung up on maths for this thread.

 

[Instine]

BTW thank you for moving Crother's thread.

 

[Instine]

Are you still there JesseM, AlphaNumeric, George Jones? Should I continue with my philosophical rant, and and get it out of the way. Or is it already bringing all good physicists out in a rash?

 

[Instine]

I'm going to keep going anyway, as I have the time now, and may not tomorrow.

All your arguments seem to be based on the tacit assumption that the laws of physics as seen by him can only take into account things which he is actually capable of measuring, but you've never really provided any reasons that we should accept this assumption.

Not that he can observe, but that his universe can observe. If his universe can not observe the cause it can not observe the effect.

Who says "information" is needed to "sustain the reality" of anything in the first place?

Laplace for one. Check out causality, or causal determinism in good books. As I refrain from reading at all possible junctures, its wrong of me to act like an authority and suggest a particular book. But it is safe to say there are plenty of 'mainstream' publications dealing with this segment of philosophy. Very few disputing it in any meaningful way, as far as I'm aware.

On the quantum level this seems so. Schroedinger's cat... (Naturwissenschaften 1935 E. Schrödinger). Here reality is not realized until observed. As probability waves of the constituent energetic particles/wave-particles remain uncolapsed. Though it highlights the issue that all elements of a system are 'an observer', this sill means that the effect of events beyond observation (beyond the shell) are never to be realized and have effect within the shell. The uncertainty principle (Werner Heisenberg 1927.) would not hold if you were certain that something will not be observed during a give period. Even the speed of light itself, is always relative to the observer. What speed should it be for light that is never observed (e.g. that falling into the shell from outside)? Without observation, Physics itself is annihilated.

It is from this belief and my belief that no information can pass through the shell, and that there does not exist the information within the shell to cause the shell, that I deduce, if the cause of a phenomenon (the shell) can not be observed from any point within the observable universe, that phenomenon (the shell) can not exist in that universe in any meaningful way, and the shell must go. But where? or to be replaced by what? c speed expansion and rapid cooling? Logical annihilation (whatever that means in reality)? Like I say - what happens next?

This is not to say that all is predictable, but that all is predictable in theory, if you could observe from any point at any scale at any time within your universe. But you can not observe infinite properties, so you can not observe the infinitely dense shell, so it and its associated phenomena cannot exist in your universe.

Over simplifying: Without observation there is no physics, with no physics there is no phenomena, with no phenomena no reality.

As no information passes through the shell, how can the reality of phenomena exterior to the shell, communicate the cause of any alterations to the reality of the interior? If no information within the shell can proscribe the precise reality of the shell, then what is?

Yes reality could be yet more complex. And reality unobservable and inconceivable to us may make this all irrelevant, bust I'm assuming that not to be the case. Quite why I'm not sure, but its found in my optismism, that I touched on earlier.

Thoughts? JesseM? You raised the request for qualification of assumption first. I've not given much, and its far from proof, but it has basis.

Fingers crossed that's the philosophy over with. And although I'm more than willing to argue these points further, I will try to keep answers brief, and when they warrent it, maybe move them to the appropriate board, in order to keep the bulk of this discussion physics, and here. That is if people are still reading, and reponding? Thank you again to the modorators for allowing this nasty philosophy stuff to be descussed here, as it has allowed me at least (and I hope others reading) to learn some new physics. Zero thick discs, and much of the detail re scale (from Prevec et al) have been news to me. AlphaNumeric was the first to spot the Cosmic Censorship link (which pointed out a mistake I'd made in my physics, not my philosophy), which may not have happened on a different forum. Like I say, I've been gently pondering this for years, so thankyou all very much! And keep it coming.

 

[Instine]

Back to the physics of it! (BTW I'm getting more and more aware that I'm the only one posting ) Hey ho...


In response to Prevect's suggestion that we use a Dust model to analyse this case, there's call in http://216.239.59.104/search?q=cach...ouse@maths.ox.ac.uk&hl=en&gl=uk&ct=clnk&cd=6" to avoid this. As prior to collapse pressures are indeed a major player in the physics of the collapsing shell. And of cause the dust model is collisionless.

But I have come up with a more realistic (though still very silly indeed) scenario.

1) Send a bomb into the centre of a REALLY BIG dust nebula.
2) Blow it up. Then fly to the location of the explosion.
3) Wait...

AH! I was beaten to it by a year! Tod (1992).

But Penrose sais:
"A closely related situation was studied by Tod (1992). In this example, there is acollapsing shell of 'null matter' (a delta-function shell of massless dust) which fallinto a region of Minkowski space that it surrounds. The mass density can varyarbitrarily with spatial direction, and the (convex, smooth) shape of the shell, at oneparticular time, can also be chosen arbitrarily. By choosing this shape to be a suitableprolate ellipsoid it is not hard to ensure that caustics in the collapsing shell - andhence singularities - arise before there are any trapped surfaces. The description isgiven in terms of standard t = const. hypersurfaces in the interior Minkowski space.Nevertheless, the situation is completely consistent with the conventional picture ofgravitational collapse to a black hole. Trapped surfaces do in fact occur in the space-time, but not until after the t-value at which singularities arise. This is again similar tothe Shapiro-Teukolsky situation, and there is no reason to expect a violation of cosmiccensorship"

However this is just a collapse, what if we gave it a push too? What about the crushing explosion?

 

[JesseM]

All your arguments seem to be based on the tacit assumption that the laws of physics as seen by him can only take into account things which he is actually capable of measuring, but you've never really provided any reasons that we should accept this assumption.

Not that he can observe, but that his universe can observe. If his universe can not observe the cause it can not observe the effect.

But this only makes sense if we define the region inside the singular surface to be a different "universe" than the region outside--it seems like circular reasoning to me. Why not consider both regions as part of the same universe? And if you think they must be considered separate, then again, could you please address the question of whether the region outside the expanding true vacuum bubble must also be considered a separate universe from the region inside it, and whether you would therefore conclude that the scenario of our being destroyed by such a bubble is a priori impossible?

Who says "information" is needed to "sustain the reality" of anything in the first place?

Laplace for one. Check out causality, or causal determinism in good books.

Laplacian determinism has nothing to do with the idea you seem to be proposing that if a particular observer situated within the universe doesn't have access to information about certain facts, then they cannot affect him. Instead of taking the perspective of any particular observer, Laplace imagined a demon with omniscient knowledge of everything in the universe--this is basically similar to the "godlike perspective" I was referring to earlier:

Isn't GR based on taking a sort of godlike "objective" point of view where we can see the whole of spacetime at once, even if no individual observer within spacetime has access to all this information? And from this godlike point of view, the observer within the singular surface is also within the event horizon that surrounds the singular surface, even if this horizon cannot be seen by him. As I understand it, "cosmic censorship" is supposed to be based on whether an observer really is within an event horizon or not, not whether or not he can know if he is. It seems like you're conflating epistemology with ontology, so to speak...maybe you could justify this in terms of the centrality of information in quantum mechanics or something like that, but your perspective at least needs to be argued for rather than just taken for granted.

Do you reject the idea, for example, that if an omniscient Laplacian demon knows that the singular surface lies within an event horizon, then that can determine whether or not cosmic censorship applies within the singular surface? If so, then your arguments don't seem to have much to do with Laplace's idea that complete knowledge of the state of the entire universe would be enough to deduce everything about the past and future.

On the quantum level this seems so. Schroedinger's cat... (Naturwissenschaften 1935 E. Schrödinger). Here reality is not realized until observed. As probability waves of the*constituent*energetic particles/wave-particles*remain uncolapsed. Though it highlights the issue that all elements of a system are 'an observer', this sill means that the effect of events beyond observation (beyond the shell) are never to be realized and have effect within the shell.

But the cat is affected by events beyond his observation up until that moment--consider the moment that the experimenter opens the box! If the box was truly isolated from the outside world up until the moment the box was opened (probably a practical impossibility for such a large hot system, but it's stipulated by the thought-experiment), then an observer inside the box could not in principle know what was going on outside before then. By your own logic, doesn't that mean the inside of the box is now a separate "universe", and can never possibly affected by events in the other universe outside the box?

The uncertainty principle (Werner Heisenberg 1927.) would not hold if you were certain that something will not be observed during a give period.

Sure it would. The uncertainty principle has nothing to do with knowing whether or not an measurement will happen, it has to do with the impossibility of simultaneously measuring certain variables like position and momentum.

Even the speed of light itself, is always relative to the observer.

It's relative to a coordinate system.

What speed should it be for light that is never observed (e.g. that falling into the shell from outside)? Without observation, Physics itself is annihilated.

Again, physics generally tries to describe the universe in an "objective" way--the same sort of omniscient, objective godlike perspective I mentioned earlier (with the possible exception of quantum mechanics, although most 'interpretations' of QM besides the Copenhagen interpretation try to restore it). Whether or not an actual physical observer is present in a given region is irrelevant to the theoretical question of what would happen in a certain region of spacetime with a given metric and distribution of matter/energy. We can model the situation just fine from our perspective "outside" of spacetime, even if we can see from the model that different regions of the spacetime we're modelling would not have information about each other, and therefore observers in those regions would not share our complete knowledge of the situation.

Over simplifying: Without observation there is no physics, with no physics there is no phenomena, with no phenomena no reality.

And again, this seems like a conflation of epistemology--what we limited observers can know--with ontology--what is really true.

As no information passes through the shell, how can the reality of phenomena exterior to the shell, communicate the cause of any alterations to the reality of the interior?

As no information passes through the walls of the box in the Schroedinger's cat experiment until it is opened, how can the reality of the interior ever be affected by outside actions (like opening the box)? As no information passes from the inside of the true vacuum bubble to the outside false vacuum until the wall of the true vacuum annihilates it, how can the reality of the false vacuum region ever be affected by the creation and growth of the bubble?

 

[Instine]

In short - yes. I agree with most of what you say here but not all. I'll set up a new thread on a philosophy board to continue this side of things.

But this only makes sense if we define the region inside the singular surface to be a different "universe" than the region outside

Essentially this is what I was attempting to justify. Obviously there's more to do there. I'll post the link to the new thread tomorrow. I'm off for an early night.:zzz:

 

[Instine]

Right - I've set up a https://www.physicsforums.com/showthread.php?t=124970".

Not had/got time to give much of an answer yet, but more will come.

 

[coalquay404]

Apologies for digging this thread up after so long. However, on reading Crother's posts, it's clear that he misunderstands some reasonably elementary concepts behind exact analytic solutions to the field equations. That said, he does make a reasonably exact point about multiple black hole solutions to Einstein's equations (although, I suspect, for reasons which are very wrong).

In spite of the impression that many people have, multiple black hole solutions is a reasonably delicate area. There's a copious amount of literature on the subject, all of which is well known, so I won't repeat it here. However, an interesting point is that Einstein's equations *do not* admit multiple black hole solutions in asymptotically flat, vacuum, static spacetimes. There's a huge and interesting selection of research on this area, much of it employing the use of Green's functions at infinity to analyse the spacetime (it also has a very close connection with the Riemannian Penrose inequality, but I digress). The canonical paper on this subject is Non-Existence of Multiple Black Holes in Asymptotically Euclidean Static Vacuum Space-Time, Bunting & Masood-ul-Alam, Gen. Rel. and Grav. 19(2) (1987).

 

[pervect]

However, an interesting point is that Einstein's equations *do not* admit multiple black hole solutions in asymptotically flat, vacuum, static spacetimes.

I'd probably have to special order the reference you quoted. I'm probably not interested enough to spend money on the topic at this point, but I'd be interested in any comments you have about how one tells when solutions are different. Suppose, for instance, we have two solutions, which are related by a diffeomorphism - are they "different", or the "same"?

More to the point,what about the case when a diffeomorphism exists that maps the points of one solution to a subset of the points of another solution? Are the two solutions "different"? How do we express this more exactly?

 

[George Jones]

Hi Pervect, I think you're reading this the way I originally read it, however, coalquay404 is talking about one spacetime in which there are two (or more) black holes, i.e, one solution to Einstein's equation that describes multiple black holes. This is what Crothers talks about in the first paragraph of post #53.

 

[coalquay404]

George Jones is correct. What I was referring to was that one can't develop an exact solution of the field equations which describes a spacetime in which there are two or more black holes. Sorry for the confusion.