Hollow spherical blackhole thought experiment

[Crothers]

Here are extracts from my previous posts.

"I refer again to Schwarzschild's paper. I note that the issues I raised with respect to this have not been addressed. One cannot make the arbitrary moves on his variables from which the black hole has been conjured. Examine his equation (14), his arguments to his eq. (6) and note the points I made in my previous post. Clearly, the standard line-element by which the black hole is conjured up is inconsistent with Schwarzschild's true solution, for the fact that the manipulations of his variables are mathematically inadmissible. The standard metric is a corruption of Schwarzschild's solution, and is consequently geometrically invalid. Schwarzschild's true solution is regular on 0 < r < oo."

"I'm interested to see if the black holers will rigorously address the issues I have raised concerning the corruption of Schwarzschild's solution and the alleged requirement in General Relativity for singularity at an unbounded Kretschmann scalar, instead of diverging into other matters."

"I therefore require first your attempts to rigorously prove the legitimacy of the arbitrary modification of Schwarzschild's true solution, which is regular on 0 < r < oo, in relation to the form you call Schwarzschild's solution and your, or anyone's proof (even Wald's, or Thorne's, or Hawking's, or Penrose's etc, but they have never given one) proof that GR necessarily requires singularity at an unbounded Kretschmann scalar."

These are the proofs I have asked for. Please provide them before proceeding to other things such as the K-S alleged extension.

As for Einstein's gravitational field, it is clear that satisfaction of the field equations is necessary but insufficient. For example, the solution must be asymptotically Minkowski. It must also satisfy the intrinsic geometry of the metric since a geometry is fully determined by the form of its metric. What is the intrinsic geometry of the metric? That will begin to become apparent when you or others attempt to provide the rigorous proofs I have asked for.

 

[Instine]

hmmm.

The thread is slipping here. As OP author, I'd like to draw a line under this issue.

1) I'm a 'black holer' and though your concerns are duly noted, Crothers, I'm not changing my view drasticly on this note
2)

I offer only citations of relevant papers and mathematical truths.

This is not so. Abstracted applied maths is not apriory, as it is applied! This is philosophy, and not the kind we need to be discussing. And again, I don't want the thread bumped.
3) It has little to do with the thought experiment at hand, as we are assuming the plausability, at least, of black holes, in order to discuss this topic.

So thanks for the input, but the the whole 'do black holes really exist' should be on another thread, possibly another forum.

So what of the question? How does an event horzon, governed by a singularity, behave, if no information exists about it (other than human memories) in the universe that contains it?

There's plenty to go at there without arguing very old ground.

Cheers

 

[Instine]

BTW - on a side note, I think I'm getting away with 'promoting a personal theory', as I'm not really, its a participatory thought experiment, which allows you guys to teach me something (which you are) and vice versa. So although this may bend forum rules I hope I don't break them.

However I do have another theory I'd like to discuss with others. And it doesn't fit into a thought experiment. And is much more likely to bend the rules beyond where the moderators are lilely to want it to go. So where can/should I discuss it? Is there somewhere on this forum? Or does anyone know somewhere else more suitable. It is a form of a unified theory, but is so far purely a model, with no work having been done to test it. Not only would I be promoting my personal theory, some may see it as a little crackpotish too. So wheres good to go. Obviously I don't just want to expound it to other 'crackpots' on MySpace, but folk who know what they're talking about, and this has been one of the best forums I've found that fits this discription. Sorry for the off topic.

All suggestion welcome, but again, back the the topic at hand

 

[selfAdjoint]

However I do have another theory I'd like to discuss with others. And it doesn't fit into a thought experiment. And is much more likely to bend the rules beyond where the moderators are lilely to want it to go. So where can/should I discuss it? Is there somewhere on this forum? Or does anyone know somewhere else more suitable. It is a form of a unified theory, but is so far purely a model, with no work having been done to test it. Not only would I be promoting my personal theory, some may see it as a little crackpotish too. So wheres good to go. Obviously I don't just want to expound it to other 'crackpots' on MySpace, but folk who know what they're talking about, and this has been one of the best forums I've found that fits this discription. Sorry for the off topic.

There is a place on PF that was created for exactly what you describe. It's called the Independent Research (IR) forum: https://www.physicsforums.com/forumdisplay.php?f=146. It has very strong guidelines for presentation of your theory, basically you have to "write it up" almost as if you were preparing it for a peer reviewed journal.

 

[Instine]

Thanks for the pointer. I'll check it out, although I'm more up for an open forum, than an electronic peer review system. Being dyslexic, I find 'writing up' prohibitively frustrating. Where as chatting more freely I make fewer mistakes, and can correct them as they are pointed out.

Any thoughts on where there may be such a place. If not, I'll likely give IR a bash anyway.

 

[Instine]

As a quick 'show of hands' who's still actually pondering this one, and who thinks its soluble?

And if insoluble, what do you think this suggests?

 

[pervect]

As a quick show of hands, I don't see a prima facie case for a paradox at all.

 

[pervect]

To avoid hijacking the OP's thread, I've moved my reply to Crother. I suggest that further discussions of the issue take place in this thread.

https://www.physicsforums.com/showpost.php?p=1019615

 

[George Jones]

There does exists a solution for a collapsing thin, pressureless, spherical shell of matter. Outside the shell, spacetime is Schwarzschild, inside the shell, spacetime is Minkowski.

References: Poisson's book, section 3.9; Israel, Nuovo cimento, 1966.

 

[JesseM]

There does exists a solution for a collapsing thin, pressureless, spherical shell of matter. Outside the shell, spacetime is Schwarzschild, inside the shell, spacetime is Minkowski.

Again, Instine isn't talking about a spherical shell of matter with finite volume. He's talking about a weird form of 2D singularity with zero volume but finite area and mass (and therefore infinite density, just like a point singularity or a ring singularity), shaped like the surface of a sphere. I still am not sure whether such a thing would even be allowed in GR, and even if it is there may not be any way it could form naturally.

 

[George Jones]

Again, Instine isn't talking about a spherical shell of matter with finite volume. He's talking about a weird form of 2D singularity with zero volume but finite area and mass (and therefore infinite density, just like a point singularity or a ring singularity), shaped like the surface of a sphere. I still am not sure whether such a thing would even be allowed in GR, and even if it is there may not be any way it could form naturally.

My short description was not very clear, but this is what I mean. It's similar to electromagnetism, where a surface charge density is an often-used and useful approximation to physical reality.

 

[pervect]

Again, Instine isn't talking about a spherical shell of matter with finite volume. He's talking about a weird form of 2D singularity with zero volume but finite area and mass

Suggestion: try thinking about the Newtonian case first.

Some suggested thought experiments:

1) Using Gauss's law, calculate the surface gravity of a spherical shell of total mass M and radius r. Show that the result depends only on the total mass M and the radius r - that it is not a function of the thickness of the shell, or the density. Show that the result for the surface gravity is finite if M and r are finite.

2) Because the surface gravity does not depend on the thickness t, taking the limit as t->0 is trivial. If the shell is very thin, show that the surface gravity remains finite, even as thickness approaches zero.

2a) If you want extra convincing, try figuring out the gravity of an infinite plane sheet of thickness t and density rho. Show that it depends only on the product of rho*thickness specifically

acceleration = 2*Pi*G* (rho*thickness)

where rho is the density / meter^3, and thickness is the thickness of the disk in meters.

3) Calculate the escape velocity for the sphere in addition to the surface gravity. As long as the Newtonian escape velocity is << c, one expect that Newtonian gravity will work just fine.

4) Make a rough order of magnitude estimate of when the object will become a black hole by computing when the escape velocity reaches the speed of light.

5) For a full GR treatment -- consider that Birkhoff's theorem says that any spherically symmetric vacuum solution of Einstein's equation will be the Schwarzschild solution. Re-read George's response with this in mind.

 

[JesseM]

My short description was not very clear, but this is what I mean. It's similar to electromagnetism, where a surface charge density is an often-used and useful approximation to physical reality.

Suggestion: try thinking about the Newtonian case first.

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. 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?

5) For a full GR treatment -- consider that Birkhoff's theorem says that any spherically symmetric vacuum solution of Einstein's equation will be the Schwarzschild solution. Re-read George's response with this in mind.

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?

 

[Instine]

This is a very hard line to ballance upon, but now you guys are not being philisophical enough.

I'm not interested in the matematical solution. As it is not the maths I'm worried about. I'm worried that FP is in a universe surrounded by singularity, BUT there is not enough information in that universe to describe the singularity, and thereby proscribe what happens next.

So again, can anyone say what happens next, as seen by FP.

Again the silly graphic.

 

[Instine]

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?

I've forgotn who I was repliing to, but this was suggested by someone earlier. My reply is at https://www.physicsforums.com/showpost.php?p=1018820&postcount=60"

(reading back it was choron who first noted this issue)

There's an issues here isn't there?...

 

[JesseM]

I'm not interested in the matematical solution. As it is not the maths I'm worried about. I'm worried that FP is in a universe surrounded by singularity, BUT there is not enough information in that universe to describe the singularity, and thereby proscribe what happens next.

Why do you think there is "not enough information in that universe to describe the singularity"? Do you think there is enough information in the universe outside the singular surface to describe it? Even if it's true that worldlines end when they hit the singularity and no information can pass between the two regions of spacetime, in both cases you have a region of spacetime with a "border" defined by the singularity, there's no reason to treat the two cases differently. If you imagine making the surface larger and larger, in the limit as the radius approached infinity the surface would just look like a flat wall dividing 3D space into two regions, and obviously in the case of an infinite flat singular surface you wouldn't treat the two sides differently.

 

[Instine]

Why do you think there is "not enough information in that universe to describe the singularity"? Do you think there is enough information in the universe outside the singular surface to describe it? Even if it's true that worldlines end when they hit the singularity and no information can pass between the two regions of spacetime, in both cases you have a region of spacetime with a "border" defined by the singularity, there's no reason to treat the two cases differently.

I've had a crack at explaining this bit before, but I don't think folk had got there heads round the rest of the problem at that point. So here's anothjer try:

When 'outside' a black hole, the universe can 'feel' the foces of its gravitational field, you can observe lensing around it, etc...

Although there is no information passing from the singularity, to an onlooker, its mass and other properties can be induced by making 'related' observations.

When 'inside a perfectly sperical black hole' all of these 'tricks' are taken from you. Not only is the mass (and thereby the cause) of the singularity beyond your world, its effect on your world is not observable. No cause, or effect... No singularity?...

Any clearer?

 

[Instine]

OK

I've been pondering this, on and off for many years and only now does this strike me. There woould be no inner event horizon!

Causing a naked singularity!

Again thanks for the chats you fellas. It was only describing it, that made me see this.

 

[Instine]

This requires a new silly picture:

 

[JesseM]

I've had a crack at explaining this bit before, but I don't think folk had got there heads round the rest of the problem at that point. So here's anothjer try:

When 'outside' a black hole, the universe can 'feel' the foces of its gravitational field, you can observe lensing around it, etc...

Although there is no information passing from the singularity, to an onlooker, its mass and other properties can be induced by making 'related' observations.

When 'inside a perfectly sperical black hole' all of these 'tricks' are taken from you. Not only is the mass (and thereby the cause) of the singularity beyond your world, its effect on your world is not observable. No cause, or effect... No singularity?...

Any clearer?

But if worldlines do indeed terminate at the singular surface (and if they don't, then there'd be no problem with the two regions exchanging information), then the observer inside could still deduce the size of the singularity by sending probes out and seeing when they stop transmitting. And by using this method to see how quickly the singular surface was collapsing to a point, is it possible he could deduce its mass as well?

Anyway, from a more philosophical point of view, just because you can't measure something from where you are doesn't mean it can't affect you? Check out the wikipedia entry on idea of a vacuum metastability disaster, where a bubble of lower energy vacuum would expand outward at close to the speed of light--other sources I've read, like this one and http://www.phys.utk.edu/rhip/Articles/RHICNews/Essay%20Will%20Brookhaven%20Destroy%20the%20Universe%20Probably%20Not.htm , say it would expand at the speed of light, I'm not sure who's correct--destroying everything in its path. If it actually moved at the speed of light, there's no way any measurements before it hit us would give us warning of its approach, but you wouldn't say that means it's "not part of our universe" and thus can never harm us, would you? Similarly, even if the guy in the center of the collapsing singular surface could have no warning of its approach, I don't see why that should make it plausible that he's in some alternate universe where the surface won't collapse in on him and crush him into a point singularity.

 

[Instine]

A wonderful reply JesseM

But if worldlines do indeed terminate at the singular surface (and if they don't, then there'd be no problem with the two regions exchanging information), then the observer inside could still deduce the size of the singularity by sending probes out and seeing when they stop transmitting. And by using this method to see how quickly the singular surface was collapsing to a point, is it possible he could deduce its mass as well?

I love this. This is a good point. And I'll have to ponder it. But my initial feeling is, this is too conveluted. The probes could die for other reasons.

Anyway, from a more philosophical point of view, just because you can't measure something from where you are doesn't mean it can't affect you? ...

Again good point, but I'm saying you couldn't, no matter where you where in that universe. This is a big difference.

And none of this broaches the new issue of, IF there is even a EH to cloth our inner universe's singularity. ?... Curiouser and curiouser

 

[George Jones]

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. 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?

The solution I referenced is Minkowski inside. The metric is continuous at the (hyper)surface, but it has sharp corner (think absolute value of x) there. Consequently, taking one derivative gives jump discontinuities in the connection, and a further derivative shows that the curvature tensor involves Dirac delta functions, just as you suspected.

Physically, I think this means that an extended body that falls through the surface experiences infinite tidal forces at the surface. However, if the surface is outside the Schwarzschild radius, there is no event horizon.

As for the geodesics of an infalling (non-extended) point particle - I don't know. Very interesting question.

 

[JesseM]

I love this. This is a good point. And I'll have to ponder it. But my initial feeling is, this is too conveluted. The probes could die for other reasons.

They could, but any measurements could go wrong for various reasons, including measurements of the curvature of spacetime. What we know about the universe is different from what is actually true about the universe...surely if probes keep failing when they travel a certain distance from you, there must be an objective truth about why this is happening, regardless of whether you can ever be sure of what that truth is?

Again good point, but I'm saying you couldn't, no matter where you where in that universe. This is a big difference.

But that's only because you've defined the word "universe" in a peculiar way, excluding everything that's exterior to the singular surface. In the case of the expanding vacuum bubble, if you defined "our universe" as only the false vacuum outside the bubble, then if the bubble is expanding at the speed of light it would also be true that you could never measure it before it annihilated you, no matter where you were in "our universe". Again, would you say this means it could never affect us, and rule out the possibility of our being destroyed by such a bubble a priori on "philosophical" grounds? The argument just doesn't make much sense to me.

 

[Instine]

Another diagram, with some axes to help:

 

[JesseM]

Physically, I think this means that an extended body that falls through the surface experiences infinite tidal forces at the surface. However, if the surface is outside the Schwarzschild radius, there is no event horizon.

As for the geodesics of an infalling (non-extended) point particle - I don't know. Very interesting question.

Interesting, thanks. I also wonder what effect infinite tidal forces would have on an electromagnetic wave hitting the surface, whether the wave would just be absorbed into the mass of the surface like with a wave falling into a point singularity, or whether it could actually pass through and allow communication between the inside and outside.

 

[Instine]

They could, but any measurements could go wrong for various reasons, including measurements of the curvature of spacetime. What we know about the universe is different from what is actually true about the universe...surely if probes keep failing when they travel a certain distance from you, there must be an objective truth about why this is happening, regardless of whether you can ever be sure of what that truth is?

As I say, I'm not denying you have a good point here. Like I say, I'll need to think on it some more.

But that's only because you've defined the word "universe" in a peculiar way, excluding everything that's exterior to the singular surface. In the case of the expanding vacuum bubble, if you defined "our universe" as only the false vacuum outside the bubble, then if the bubble is expanding at the speed of light it would also be true that you could never measure it before it annihilated you, no matter where you were in "our universe". Again, would you say this means it could never affect us, and rule out the possibility of our being destroyed by such a bubble a priori on "philosophical" grounds? The argument just doesn't make much sense to me.

This is where I disagree more substantially, though admittedly, its hard to explain why at such an abstract level.

But that's only because you've defined the word "universe" in a peculiar way, excluding everything that's exterior to the singular surface.

Yes and I very much stick by this. The shell singularity defines an aboslute barrier to the point that you must exclude that which 'is beyond' from any physics 'within'. Completely and without exception.

Interesting, thanks. I also wonder what effect infinite tidal forces would have on an electromagnetic wave hitting the surface, whether the wave would just be absorbed into the mass of the surface like with a wave falling into a point singularity, or whether it could actually pass through and allow communication between the inside and outside.

no chance.

 

[Instine]

Re your bubble, I don't know, is the short answer.

 

[Instine]

And yes, nice post George.

I have issue with the Dirac Delta function, but I guess its pretty much accepted orthodoxy, so I'll not go off on one.

So are you saying this precludes it from forming? As it does suggest a Censorship violation...

 

[Instine]

Apologies for the manic posting. Could you expand on your Minkowski reference Geroge. Another one that's news to me.
Cheers


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

 

[George Jones]

I have issue with the Dirac Delta function, but I guess its pretty much accepted orthodoxy, so I'll not go off on one.

A delta function can be approximated physically be a sequence of increasingly narrow and high peaks.

So are you saying this precludes it from forming? As it does suggest a Censorship violation...

Once the shell falls through its Schwarzschild radius, an event horizon forms.

By Minkowski, I mean that inside the shell, spacetime is perfectly flat - no gravitational forces.

 

[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.