We are in a Schwarzschild black hole-T or F?

[Jorrie]

It is no coincidence that our observable universe has the same radius as it would if it were a black hole, because the Schwartzschild solution for a black hole is mathematically equivalent to the equation for determining the event horizon of an observable universe.

Hi Jon. How do you get to this mathematical equivalence? I think it's coincidental, but would like to hear your rationale.

Jorrie

 

[jonmtkisco]

Hi Jorrie,

I think this http://http://arxiv.org/PS_cache/arxiv/pdf/0711/0711.4181v1.pdf" answers your question, but let me know if you disagree.

Jon

 

[Jorrie]

I think this http://http://arxiv.org/PS_cache/arxiv/pdf/0711/0711.4181v1.pdf" answers your question, but let me know if you disagree.

I don't think Melia actually claims that our present observable universe with presumably accelerating expansion has the same radius as it would if it were a black hole. That may have been the case without dark energy and with the deceleration parameter equaling zero.

From Melia's summary:

However, it may be that observational cosmology is not entirely consistent with
the condition R0 ≈ ct in the current epoch. If not, there must be some other reason for
this apparent coincidence. Perhaps the assumption of an infinite, homogeneous universe is incorrect.

Jorrie

 

[jonmtkisco]

Hi Jorrie,
Hmmm, I think I had the cosmological Particle Horizon in mind rather than the Event Horizon. The correspondence of the event horizon with the Schwartzschild radius may be a "coincidence" in a certain sense, but I think it's no more coincidental than how close the size of the observable universe is to the Hubble Volume. In both cases I think the deviation is rather small because the "S" shaped expansion curve ends up close to linear curve at our epoch.

Jon

 

[PaulR]

I am still confused by this reply of 1/22/08 by Marcus.

I am trying very hard to understand the difference between a "real" black hole and a section of space where the density satisfies the Schwarzschild formula.

As I understand from the previous answers, the single other issue reuired is that the section of space not be expanding.

To verify that I understand this point, I am positing a thought experiment. If our section of space stopped expanding, would an observer outside this section then view this as a black hole? It has the proper density. If it is not expanding, is that sufficient or would some other issue come into play.

I believe the whole confusion as to whther we live in a black hole revolves around this specific point. Everyone agrees that a 13.7 billion light year sphere is exactly the radius that matches up to the actual density to satisfy that criteria. The issue is what other criteria come into play.

As a second issue, since all space is expanding, why does this expansion not also disqualify the smaller black holes, since they must also be expanding to a very slight degree.

A third issue is - is there a theoretical maximum to the size of a black hole? Can it equal or even exceed the 13.7 billion light year radius being discussed?

 

[Jorrie]

I believe the whole confusion as to whether we live in a black hole revolves around this specific point. Everyone agrees that a 13.7 billion light year sphere is exactly the radius that matches up to the actual density to satisfy that criteria.

Everyone does certainly not agree that our observable universe comprises a "13.7 billion light year sphere". The universe is expanding and the proper radius of our observable portion is around 46 billion light years. This then means that the actual density is far less than what is required to be a black hole. The 13.7 Gly is simply how far light could have traveled since the BB.

If only our observable universe hypothetically stops expanding (an impossibility), while the rest of the universe carries on expanding, then yes, our observable universe will start to contract and possibly become a black hole sometime in the distant future.

As a second issue, since all space is expanding, why does this expansion not also disqualify the smaller black holes, since they must also be expanding to a very slight degree.

My view is that firstly, the expansion rate for a tiny homogeneous piece of space is so small that we cannot detect that. Secondly, a black hole is gravitationally bound and that overwhelms any small cosmic expansion that there may be.

 

[marcus]

Hi Paul, I think your questions in your last post are good ones. You refer back to a post of mine which may have lacked clarity or said something wrong. (I'm a retired mathematician who likes cosmology, not a professional astronomer, so I'm always open to correction from the working astronomers here.) Here's an exerpt.

...
to an observer out there 13.7 billion LY from here, things would look pretty much the same as they do here----same density of matter, same kind of galaxies, same nearly flat space.
...
if the universe stopped expanding and prepared to collapse then we would ALL be, in effect, in a black hole which would NOT have 13.7 billion LY as any kind of horizon. the WHOLE KABOODLE would be destined to collapse, all observers would realize this----that they were all inside what was going to collapse.
...
I think that's about right Paul. Someone can correct me if I've made some error. But I haven't thought much about Crunch because I don't think its in the cards.
There seems to be a consensus nowadays that the universe is on track to keep expanding indefinitely.

I am still confused by this reply of 1/22/08 by Marcus.

I am trying very hard to understand the difference between a "real" black hole and a section of space where the density satisfies the Schwarzschild formula.

As I understand from the previous answers, the single other issue reuired is that the section of space not be expanding.

To verify that I understand this point, I am positing a thought experiment. If our section of space stopped expanding, would an observer outside this section then view this as a black hole? It has the proper density. If it is not expanding, is that sufficient or would some other issue come into play.

I believe the whole confusion as to whther we live in a black hole revolves around this specific point. Everyone agrees that a 13.7 billion light year sphere is exactly the radius that matches up to the actual density to satisfy that criteria. The issue is what other criteria come into play.

As a second issue, since all space is expanding, why does this expansion not also disqualify the smaller black holes, since they must also be expanding to a very slight degree.

A third issue is - is there a theoretical maximum to the size of a black hole? Can it equal or even exceed the 13.7 billion light year radius being discussed?

That is a fascinating thought experiment. In a sense Jorrie has already responded to your post, but I am intrigued by your question and I want to focus on it.

You are NOT asking what if the universe magically stopped expanding. I think you and I both agree that then we would be destined for a big crunch. There would be no center towards which we were falling. Every point would be destined to become the singularity just as in our present space every point is the point where the big bang occurred in the past. There would be no horizon and no center anywhere. Everything would look much the same except that galaxies would be BLUEshifted. and after a while we would notice an increase in CMB temperature.

You are not asking about that, you are saying what if OUR SECTION of the universe magically stopped expanding-----a Hubble ball with us as center suddenly froze and the REST CONTINUED EXPANDING. That leaves a chasm that is widening at the speed of light and it is hard for me to picture how it could be patched within the context of GR.

Before the magic, points just outside the Hubble radius would be speeding away from us at speeds slightly faster than light, and after the magic they would continue doing so.

you know if you magnify the cheese, the holes get bigger. so, if the rest continues expanding, the hole that our piece used to fill will get bigger along with everything else.

I am not sure how the thought experiment can be done (what kind of smooth geometry fills the rapidly widening gap, consistent with GR our theory of gravity?). But if it can be patched together to work in accordance with GR then I can see how you might have our erstwhile Hubble sphere, now static, sitting in the middle of a vast emptiness.

then you would have a welldefined center that things could gravitate toward. I can well believe that a suitably positioned observer could then witness something like the collapse of a star and the eventual formation of a Schwarzschild black hole (the normal endpoint of gravitational collapse).

When and where an horizon would form would necessarily depend on the details of how one filled in the gap in the geometry. (assuming it could be done consistent with GR)

When collapse is studied dynamically they don't just use the static Schwarzschild picture (which is an endpoint of a process) and there are different sorts of horizons, different equations etc. Collapse, when studied realistically, is a research area.
===================

To respond to your other questions, that I highlighted. As far as I know there is no theoretical limit to BH size. I don't see why there would be. If the universe is spatial finite then that would seem to impose some limitation but the question is too speculative for me.

It is not the case that all space is expanding uniformly at all scales even little bitty pieces. Exansion of distances is very uneven. In some places distances are contracting. The Einstein Gr metric is dynamic and has only approximate largescale symmetries. The simplified Friedmann model is an idealization.

As I said before, to study gravitational collapse realistically uses other equations besided the static Schwarzschild metric, which is also an idealization (strictly speaking it has nothing falling into it, everything has already happened). But the upshot is that yes BHs can form and do form, even though on average largescale distances are expanding as per the Friedmann solution.

Finally there was your observation about the ALGEBRAIC COINCIDENCES. You mentioned how coincidence confuses people. That is RIGHT! It does confuse us. It raises questions in my mind too! There is the coincidence that the

hubble time is approximately the same as the age of the universe

Why should, just at this moment in history, the current value of the Hubble parameter H₀ be such that
1/H₀ is approximately equal to the estimated age of expansion?

That is something I would like to hear SpaceTiger or Wallace discuss some time.

I remember somebody explained it to me by drawing a picture of the scalefactor a(t) increasing with time in a curvy way (first convex then concave) and approximating it with a straight line. And I don't thing he really explained the coincidence----essentially he was just illustrating it. I think for the time being we just live with such coincidences.

Then there is a kind of additional coincidence that you pointed out: the fact that the Hubble radius at the present time, namely c/H₀, is algebraically equal to the Schwarzschild radius in a completely different context-----a static endpoint of collapse to some central point. Personally I don't think that has any physical significance because the situations are so different. You often get the same algebraic formula turning up in different contexts. That is a coincidence that I feel is just run-of-the-mill and I don't expect any new physical insight to come out of it.

But the other one I do. It is fundamentally the similar to observing that at our moment of history the matter density and the "dark energy" density are roughly comparable---same order of magnitude. And I could be wrong, both or neither coincidence could turn out to be significant. maybe others have opinions about that.

anyway thanks for the interesting questions!

 

[Haelfix]

"The Hubble time is approximately the same as the age of the universe".

Its very close. In principle there is energy and matter related correction factors in lambda CDM, that you can calculate starting from the Friedmann equation. For a set of different parameters you will in general get a different correction (its done numerically). Typical correction factors are like 1.5-.6, and with WMAP values, about .99.

Coincidence that this is very nearly 1? Probably, its not particularly finetuned and I see no good reason for somethign else, nor why that would be important.

 

[marcus]

"The Hubble time is approximately the same as the age of the universe".

Its very close. In principle there is energy and matter related correction factors in lambda CDM, that you can calculate starting from the Friedmann equation. For a set of different parameters you will in general get a different correction (its done numerically). Typical correction factors are like 1.5-.6, and with WMAP values, about .99.

Coincidence that this is very nearly 1? Probably, its not particularly finetuned and I see no good reason for somethign else, nor why that would be important.

If I understand the post, I think on balance I tend to agree with you.
If the prevailing LCDM model is right then it is clearly a mere coincidence that the Hubble time and the age of the universe both happen to be about 13.7 billion years!

If the LCDM model is right, we expect the Hubble time to plateau at 16 billion years, while the age of the universe marches steadily onwards.

So when expansion is 32 billion years old, the age will be TWICE the Hubble time, instead of almost exactly equal to it. Also a mere and meaningless coincidence.

===================

That said, it remains a bit spooky that we should just happen to be observing the world at the moment when the age and the Hubble time appear almost exactly equal. On balance I tend to discount coincidences like this, but I suppose a striking one could on occasion be a signal that our accepted models aren't getting the full picture. The coincidence which cosmologists like best to point out, as I recall, is the fact that matter density (0.27) and dark energy density (0.73) are, if we go by the standard LCDM model, roughly the same order of magnitude. According to LCDM, during much of the past matter has dominated and in the future dark energy will increasingly dominate as matter thins out. So we just happened along at about the time the rising and the falling curves crossed.

I'm not suggesting we discuss these other coincidences, certainly not in this thread. I mention them to give perspective on the topic----which is the "are we in a black hole?" confusion. At least to some people who responded in the poll, the Hubble radius of 13.7 billion lightyears looks like the Schwarzschild radius of a different situation. It may help to generalize a bit and notice that sometimes coincidences are just that. Striking but physically unimportant.

 

[Haelfix]

Certainly the fact that the aotU is so close to the Hubble time is closely related to the better question of why matter and DE are on the same order of magnitude. The correction factor integral is particularly unlovely and I see no deep reason whereby you can reverse the argument and use it to generate exact cosmological parameters so that the factor is identically 1 (some hidden mechanism say), so yea probably coincidence hinging on the resolution of the other question.

As to why DE and matter are so damn close, I am less sure of. There very well could be something deeper at play there. Certainly, you can appeal to the anthropic principle to bound yourself into some interval (and that's one of the few places where its a valid argument) and that makes the 'coincidence' a little more palpable, but it is a little bit uncanny even then. Open question.

 

[marcus]

...

As to why DE and matter are so damn close, I am less sure of. There very well could be something deeper at play there. Certainly, you can appeal to the anthropic principle to bound yourself into some interval (and that's one of the few places where its a valid argument) ...

You might be interested in this analysis, if you haven't seen it already. Kind of in line with what you said.

http://arxiv.org/abs/astro-ph/0703429
The Cosmic Coincidence as a Temporal Selection Effect Produced by the Age Distribution of Terrestrial Planets in the Universe
Charles H. Lineweaver, Chas A. Egan
(Submitted on 16 Mar 2007)

"The energy densities of matter and the vacuum are currently observed to be of the same order of magnitude: (\Omega_{m 0} \approx 0.3) \sim (\Omega_{\Lambda 0} \approx 0.7). The cosmological window of time during which this occurs is relatively narrow. Thus, we are presented with the cosmological coincidence problem: Why, just now, do these energy densities happen to be of the same order? Here we show that this apparent coincidence can be explained as a temporal selection effect produced by the age distribution of terrestrial planets in the Universe. We find a large (about 68 %) probability that observations made from terrestrial planets will result in finding \Omega_m
at least as close to \Omega_{\Lambda} as we observe today.
Hence, we, and any observers in the Universe who have evolved on terrestrial planets, should not be surprised to find
\Omega_m \sim \Omega_{\Lambda}.
This result is relatively robust if the time it takes an observer to evolve on a terrestrial planet is less than about 10 Gyr."

 

[jonmtkisco]

I'm finding something screwy about this whole subject. Like Marcus, I had understood the current Event horizon to be about 16 Gly, as shown in Figure 1 of http://http://www.mso.anu.edu.au/~charley/papers/DavisLineweaver04.pdf" . As compared to the Particle horizon which is the radius of the observable universe, at about 46 Gly.

However, my spreadsheet calculations show that the Schwartzschild radius is equal to or greater than the actual radius of the total mass/energy at every actual radius equal to or greater than 14 Gly. Thus ANY slice of the universe with a radius larger than 14 Gly would meet this simplistic definition of a black hole.

My calculation is as follows:

14 Gly radius = 1.32E+26 meters radius = 9.73E+78 cubic meters volume. The average density (including matter and dark energy) is 9.17E-27 kg/cubic meter. Multiplying volume * density calculates a total mass/energy (within that radius) of 8.92E+52 kg. The Schwartzschild radius of that mass = 1.32E+26 meters. Schwartzschild radius being:

R_{s} = \frac{2GM}{c^2}

If you do this simple calculation on a spreadsheet, you'll see that actual radius is less than the Schwartzschild radius at every radius larger than 14 Gly; obviously that is because mass increases in proportion to the cube of the radius. The radius of our observable universe (Particle horizon) is a full order of magnitude more compact than its Schwartzschild radius. By that measure our Event horizon is a black hole inside another black hole... and so on ad infinitum.

Based on this analysis, I see nothing meaningful in trying to correlate any specific radius (such our 16 Gly cosmic Event horizon) with our Schwartzschild radius.

Jon

[Edit: p.s., I think Melia defines his term "Cosmic horizon" R_{0} to be the same as the 14 Gly Schwartzschild radius I calculated. As he says, it also = c/H_{0}.]

 

[marcus]

I'm finding something screwy about this whole subject. Like Marcus, I had understood the current Event horizon to be about 16 Gly, as shown in Figure 1 of http://http://www.mso.anu.edu.au/~charley/papers/DavisLineweaver04.pdf" . As compared to the Particle horizon which is the radius of the observable universe, at about 46 Gly.

However, my spreadsheet calculations show that the Schwartzschild radius is equal to or greater than the actual radius of the total mass/energy at every actual radius equal to or greater than 14 Gly. Thus ANY slice of the universe with a radius larger than 14 Gly would meet this simplistic definition of a black hole.
...

Does anybody (besides possibly some newcomers to the subject) actually think that is the definition? I agree with the spirit of your calling it a simplistic definition. Personally I would not call it a definition of any sort.

IMO a black hole is not merely any spherical region of space with a radius
2GM/c² where M is the mass of the material which the region happens to contain at the moment.

A region satisfying that condition will, under certain circumstances, collapse towards the center of the sphere and eventually form a black hole. But we've heard plenty of discussion in this thread to the effect that circumstances have to be right for this to happen. I think you would probably agree, Jon.

I would advise not basing anything on the paper of Melia. His field is observational astronomy, not cosmology. His use of language, when he ventured into cosmology, was idiosyncratic----eccentric----and unfortunate. His paper has some attention-getting features but I do not expect it to be much cited by other scholars. We will see.

======================
It is good that your spreadsheet gets the Hubble radius (approx 14 GLY) as the hypothetical Schwarzschild radius of a collapsed body whose mass equals the mass (including dark energy) contained in the Hubble sphere. this is just an algebraic thing. the two quantities work out to be algebraically identical. so that shows your spreadsheet is working properly.

======================

Based on this analysis, I see nothing meaningful in trying to correlate any specific radius (such our 16 Gly cosmic Event horizon) with our Schwartzschild radius.

I totally agree with your conclusion!

Jon, thank you for going through this so thoughtfully. Your conclusion suits me to a T (except that i do not use a T in spelling Schwarzschild ---Germans give the letter z a "ts" sound so they don't need the T in that phonetic context.)

 

[jonmtkisco]

Hi Marcus,

Yes my point is that trying to correlate our cosmic Event horizon with a Schwarzschild Event horizon makes no sense. It makes no sense because the two horizons are at different distances. It also makes no sense because our Schwarzschild radius can be defined only by a minimum radius at 14 Gly; its maximum radius is indefinite or infinite. Conceptually there is no such thing as a black hole whose event horizon stretches from a minimum radius outward to infinity.

[Edit: I should also point out that the two Event horizons have essentially opposite meanings. A Schwarzschild Event horizon is the distance at which an infalling photon can't escape outwards , given infinite time. The cosmic Event horizon is the point at which an infalling photon can never reach us (inwards, at the observation center) given infinite time. Since they define two different phenomena, there's no reason to think they have anything to do with each other, other than sharing a confusingly similar name.]

So I think this helps establish your point that our universe cannot be described as a black hole in any meaningful way. Besides, as we discussed previously, the Schwarzschild metric was never intended to apply to an expanding non-point mass such as our universe, and is simply mathematically incapable of explaining it. As far as I'm concerned, the case is closed.

I'm willing to give Melia a chance to make his case, regardless of his credentials. But I don't think he makes his case well in the cited paper. His version of a scaling solution for the cosmological constant is interesting but "far out" by normal standards. His reference to our minimum Schwarzschild radius as "the cosmic horizon" makes no sense to me; he fails to explain why it is a "horizon" at all, let alone the most significant one.

He claims that as R \rightarrow R_{0}, spacetime curvature increases because increasingly more mass-energy is enclosed by the sphere of that radius. That seems wrong to me; normal expansion itself (by Einstein-de Sitter or cosmological constant) obviously does not automatically cause a flat universe to quickly become significantly curved. And simply moving further away from Earth does not cause the local curvature to change, once the threshold of homogeneity is crossed. The average curvature should be the same at any such distance. Therefore I see no source for the time dilation he asserts. He says that it is physically impossible for us to see anything occurring beyond R_{0}, but he doesn't give a convincing explanation why that's so. I don't recall any other cosmologist making that specific claim, and it seems entirely inconsistent with the excellent Davis & Lineweaver paper.

Jon

p.s., "Schwarzschild" has so many extraneous letters in it that I guess I err on the side of including even more!

 

[PaulR]

Thank you for understanding my point of view. As you correctly state, I am trying to focus on one specific section of space. I avoid using terms like Event Horizon specifically to return focus to a 13.7 billion light year section of space, knowing the universe is much bigger. Many of the discussions seem to address a larger volume. But I believe the original question did not require that the whole universe be a black hole – only where we live.

We all agree that the density of the contents of this sphere satisfies the Schwarzschild formula for black holes exactly within our known accuracy of measurement. I assume this is the reason why the question was posed.

We also agree that space is expanding. As I understand it is this expansion that is the only reason why we are not in a black hole.

Before going further, I understand that a black hole is not the same as a singularity. For a black hole to exist there is only the criteria that there be enough mass to bend light inward so nothing can escape. A black hole comes into existence the moment enough mass gathers within a radius. There are two other ideas that people associate with black holes, but neither are essential.
1. A black hole can form when a massive star collapses to a size smaller than the Schwarzschild radius. However black holes can also form if a bunch of matter comes together. For instance a large number of neutron stars circling in close orbit can form a black hole.
2. The gravity in a black hole is so strong that everything inside collapses to a singularity. Again, this is a future event, not a determining factor. It takes time for all that stuff to collapse since matter attracted by gravity must travel at less than the speed of light. An outsider experiences a black hole when it is formed, not when its interior has collapsed to a singularity.

I make these points to help explain my though experiment. Specifically if a 13.7 billion year section of space with the proper mass was not expanding, an outside observer would immediately see a black hole. But the inside would not immediately be a singularity. In fact those at the center, just as someone in a hole at the center of the Earth would not feel any gravity. The collapse would start at the edge and proceed slower than the speed of light. Thus in a 13.7 billion light year sphere, the singularity would occur after considerably longer than 13.7 billion years – no need to worry too soon.

As to what happens outside, consider a smaller example. If a large enough group of galaxies came close enough, they would form a black hole. Yet immediately before forming a black hole, the space around the galaxies was expanding. After becoming a black hole, their internal space would stop expanding, but space outside would continue expanding. Surely this does not violate any theory. Similarly if a 13.7 billion year section of space stopped expanding, the same would apply. There is not supposed to be a magic size beyond which a black hole cannot form.

So my question is – am I right? Is it theoretically possible for a 13.7 billion year sphere to stop expanding and thereby immediately become a black hole long before any internal crush into a singularity?
And as a followup, how would someone in the center know since the initial action is 13.7 billion light years away?

Sorry for being so long winded. I am new to this type of dialog and realize how easily I can be misunderstood.

 

[marcus]

Hi Paul, I won't attempt to completely resolve your questions but will add to the discussion.

you have an idea of black hole which is not the Schwarzschild black hole that I opened the thread with and specified in the poll. Your idea is more general. A region with a horizon----that light can't get out of.

It is important to realize that in a homog isotropic universe, the mere fact that a spherical region contains enough mass that its radius equals 2GM/c^2 does not cause it to trap light. Wallace mentioned this early on. The gravitational field has no preferred direction. This does not depend on expansion. It would be true also in the unrealistic static case.

So we have to try to imagine how a spherical region with radius 2GM/c^2 could trap light. It isn't automatic.But we can still try to think about some situation like what you suggest, as a theoretical exercise. I will give it a try. I think to make things work we need to break homogeneity and have the big spherical region surrounded by a shell of comparatively empty space.

...So my question is – am I right? Is it theoretically possible for a 13.7 billion year sphere to stop expanding and thereby immediately become a black hole long before any internal crush into a singularity?
And as a followup, how would someone in the center know since the initial action is 13.7 billion light years away?

In this case I think yes. As long as the ball is effectively isolated in a huge void. (or reasonable facsimile )

But in the real universe our Hubble ball is not isolated. In the real universe things are uniform so there is no center to collapse to.
If the whole thing stopped expanding then the whole shebang would collapse. Then there would be no light-trapping horizon isolating a part of the whole. The whole uniform universe would be on its way to a crunch. Different from a black hole.

In that case doesn't matter if some particular region contains enough mass so that radius = 2GM/c^2. A particular spherical region could have far larger mass than that and still not trap light! I am talking the homogeneous case which seems to fit reality.

But if you want we can imagine that our Hubble ball is isolated by a huge surrounding void. So then it would have a center to collapse to. And we assume it stops expanding. The answer is YES it certainly traps light! And the singularity takes a while to form.

I'm not sure what the people inside would be seeing before the expansion stopped. It may depend on the model. Things could start falling towards the center long before the horizon forms and the light is actually trapped! Maybe someone else will step in and clarify.

 

[jonmtkisco]

But if you want we can imagine that our Hubble ball is isolated by a huge surrounding void. So then it would have a center to collapse to. And we assume it stops expanding. The answer is YES it certainly traps light! And the singularity takes a while to form.

Interesting Marcus. Perhaps this isolated "dust ball" would virialize, preventing a complete collapse, or at least delaying it indefinitely.

Jon

 

[marcus]

Interesting Marcus. Perhaps this isolated "dust ball" would virialize, preventing a complete collapse, or at least delaying it indefinitely.

Jon, you and Paul are prodding me or tempting me out beyond competence. I really need for Wallace et al to intervene.
I have never seen a solution worked out for this huge isolated dustball. You suggest that it might stabilize somewhat like a globular cluster-----a spherical swarm of gnats.
Each tiny gnat orbiting (so to speak) in the collective gravitational field.

My intuitive (merely intuitive) reaction is that this would NOT be stable and that the dustball would inevitably shrink. therefore collapse would be inevitable.

It takes some audacity or foolishness on my part to venture a mere intuition where i actually have seen nothing dealing with this problem.

My reasoning is that on the outside layer, at the start, the galaxies, or specks of dust, would be falling in at nearly the speed of light. They COULDN'T virialize out at that radius, my hunch is. So the cloud has to shrink. It can't continue to fill out its event horizon sphere. And once it starts shrinking (which it immediately does) they can kiss any hopes of virializing goodbye. The tendency to collapse just gets stronger.

I'd be interested if someone had some more careful analysis that contradicted this.

 

[jonmtkisco]

Hi Marcus,

Well I know less about this subject than you do, so I feel free to speculate.

It seems to me there is a chicken-and-egg problem here. If the dust ball "begins" without any pre-existing momentum, then its initial collapse velocity (including the outermost shell) is zero. So there is plenty of opportunity for it to be begin virializing while the collapse velocity remains slow. As it progressively virializes, that in itself might prevent the collapse from accelerating. So it may never get to the stage where the outer shell is collapsing at the speed of light.

I suppose that in theory a perfectly homogeneous dustball would not virialize. But since nothing is so perfect, tidal torques will occur. Then the race is on to see which prevails, the collapse acceleration or the virialization. There must be an existing equation that would solve this.

Also, I wonder, if the outer shell were collapsing at near the speed of light, would it collapse too quickly to virialize, as you suggest, or on the contrary would it gain proportionally equivalent virial velocities? I would guess that the answer has to do with how inhomogeneous the dust ball is. If it is only slightly inhomogeneous, I would expect the powerful gravitational collapse (which "feels" the gravitation of the entire dust ball) to far outweigh the competing pulls of the bevy of presumably much smaller and somewhat localized tidal torques.

Jon

 

[PaulR]

Thank you again for this detailed discussion.
As I now understand it there are in fact three criteria for a sphere to be a black hole:
1. The matter in the sphere must satisfy the Schwarzschild equation
2. The sphere must not be expanding
3. The space immediately outside the sphere must be relatively void

Are there in fact more criteria or is this the complete list? What about rotation?

As to this third criteria, how closely must it be satisfied? Most black holes have a cloud or disck of particles around them. If this mass gets too big, does the black hole then cease being a black hole?

 

[marcus]

Thank you again for this detailed discussion.
As I now understand it there are in fact three criteria for a sphere to be a black hole:
1. The matter in the sphere must satisfy the Schwarzschild equation
2. The sphere must not be expanding
3. The space immediately outside the sphere must be relatively void

Are there in fact more criteria or is this the complete list? What about rotation?

As to this third criteria, how closely must it be satisfied? Most black holes have a cloud or disck of particles around them. If this mass gets too big, does the black hole then cease being a black hole?

Hi PaulR, the title of the thread is "We are in a Schwarzschild black hole---T or F?"
If by BH you mean a Schwarzschild BH, then I don't think anything you say here is incorrect. There are at least these criteria----these conditions 1.2.3. seem OK (if you mean Schwarzschild).

Of course they might not be met by other kinds of BH. You talk about a sphere event horizon. But in some cases the event horizon is not a sphere. In some BH cases the formula R = 2GM/c^2 does not work. Knowing what model to use would require judgement in some cases, I would imagine.

Have you looked us BH in Wikipedia? If you are interested in the general subject, maybe you should start a thread like questions about BHs and see if any knowledgeable people respond. I'm not particularly knowledgeable.

When people talk about R = 2GM/c^2, I assume they are talking about Schwarzschild BH which is a rather special case---as I think your conditions 1.2.3. suggest.
To be quite correct, I suppose the criterion would not be your 1.2.3. but rather that the metric is the Schw. metric, which is a particular solution of the Einstein Field Eqn.

 

[marcus]

PaulR, I have an idea for you.
Have a look at the abstract of
http://relativity.livingreviews.org/open?pubNo=lrr-2004-10
and perhaps glance at some of the articles
(like those in section 2 introducing "dynamic horizon" and "isolated horizon"

Another introduction is this PF thread with hellfire and Stingray
https://www.physicsforums.com/showthread.php?t=138607

I think you want to understand the general question of WHEN IS A SURFACE (spherical or some other shape) going to TRAP LIGHT?
It turns out that the various black hole models were not adequate to deal with this problem since they required a highly idealized situation where one knows the whole future of the universe, among other things.

So Ashtekar developed some more flexible and useful concepts like "isolated horizon".
and "dynamical horizon". the latter can have stuff falling in, and it can be growing.
Stingray happens to be at Penn State, where Ashtekar is. You can see from the PF thread that Stingray is well versed in this business.

I am NOT well versed. But it seems clear that the Black Hole concept is the wrong tool for the job. Black hole models depict the endpoint of collapse. They are too idealized, too static, pat and inflexible. Especially this business of having to know the whole future of the universe in order to define one. Apparently what we need is an improved language---talking in terms of different kinds of horizons. (which may or may not eventually result in the formation of this or that kind of singularity, fitting this or that Black Hole model picture.)

I can't say this is easy! It seems to me like a comparatively hard topic to get into. But it is probably the only way to understand the phenomena at a dynamic, local level.
Let me know if you want to research this seriously and i will keep an eye out for source material. I know that Ashtekar has posted stuff on it more recently than this 2004 Living Reviews article.

 

[Lawrence B. Crowell]

If the universe we lived in were a Schwarzschild spacetime galaxies would be receeding away along to antipodal directions, but blue shifted and coming towards us along the plane normal to that antipodal direction. The dominant physics would be due to the Weyl curvature or tidal acceleration. We would not observe the relatively isotropic recession of galaxies.

Lawrence B. Crowell

 

[PaulR]

Thank you for this and yes I would like to learn more.

Maybe I now have enough info to understand the original question:
Are we in a BH with one of the cosmic horizons serving as BH event horizon?

In reading this I guess I made several assumptions:
1. A BH means a sphere
2. A BH means an area of space that has such strong gravity that light is captured - hence the name
3. That the Schwarzschild formula defined a BH for purposes of this question
4. That a distance of 13.7 b light years defines one of the cosmic horizons
5. That a BH does not require that a singularity currently exists - it may or may not

However I am no longer so sure I understand the question.

Could you rephrase what the original question refers to?

 

[marcus]

If the universe we lived in were a Schwarzschild spacetime galaxies would be receeding away along to antipodal directions, but blue shifted and coming towards us along the plane normal to that antipodal direction. The dominant physics would be due to the Weyl curvature or tidal acceleration. We would not observe the relatively isotropic recession of galaxies.

Lawrence B. Crowell

Great! This is the first post in this thread for a long time that really makes sense to me and is interesting. I wish I had thought to say this. Thanks Lawrence! This answers a question that may have been on several people's minds. How can we tell we arent in a BH? A LARGE black hole containing thousands of galaxies.

We if we were there would be a direction towards the collapse point, and in that direction galaxies would be redshifted because they would be accelerating faster, ahead of us, and in the reverse direction (behind us) galaxies would also be redshifted because we would be accelerating faster and escaping from them! And in the plane of direction which are abeam of us, sideways from that collapse direction (to port and starbord so to speak) galaxies would be BLUE shifted, cause we are all getting closer to each other as we approach the collapse point.

that is what makes sense to me, and I hope someone who has studied BH more than I have will correct me. One way or another I am sure it would be immediately obvious, if we were in the process of collapse forming such a large black hole. And I think this test that Lawrence suggests is probably right (not being an expert in the subject I can't be entirely sure.)

 

[PaulR]

Two points
1. If we were at the exact center, everything in every direction would look the same
2. If the collapse is just starting, we could not see it
Collapsing matter would start from a stand still and gradually accelerating, but always below the speed limit. Today we can only see what happened milions of years ago. Thus we need some other measure, or need to wait at least a billion years to see any signs.

PS - Thank you Marcus for that detailed explanation. I was struggling with the original post.

 

[geoffc]

Some of the more fascinating ideas concerning horizons are coming from condensed matter analogues. A fascinating article along those lines is by B.L. Hu entitled "Is Spacetime a Condensate?" here:

http://arxiv.org/abs/gr-qc/0503067

There is also an entire book entitled "The Universe in a Helium Droplet" by Volovik, a pdf version of which can be found here:

http://ltl.tkk.fi/wiki/images/b/bf/Volovik-book.pdf

 

[xantox]

We if we were there would be a direction towards the collapse point, and in that direction galaxies would be redshifted because they would be accelerating faster, ahead of us, and in the reverse direction (behind us) galaxies would also be redshifted because we would be accelerating faster and escaping from them!

Are you taking into account the fact that "ahead" and "behind" refer here to a timelike coordinate? Also, I suggest to consider that the interior of a black hole does not need to have a Schwarzschild metric (and certainly it does not have it if it is not empty).

 

[PaulR]

Interestingly, the Feb2 issue of Science News (which is not peer reviewed but does have a reputation) has the following on P 75:
"In a very different theory put forward by Jae-Weon Lee of the Korea Institute for Advanced Study in Seoul and his colaborators, the universe is, in effect, a giant black hole."

"Lee and his colleagues suggest that as the universe expands, it creates a cosmic version of a black hole - event horizon, a region of space from which distant observers will never see a light signal. If a particle-antiparticle pair is created at this horizon, one particle may fall toward it while the other heads toward the distant observer. In effect, the cosmic-event horizon radiates, and Lee's team says the radiation could be just enough to drive the accelerated expansion."

This raises several points.
First, the idea that there could be a black hole means that these intelligent parties do not think that the idea of a black hole is ruled out on theoretical or current observational grounds. If I understand this correctly then the best answer to the original question is - Not sure

Second - it would seem that the mere fact that the universe is expanding does not rule out a black hole, contrary to some of the discussion.

However I am aware of my ignorance so these two points are really two questions.
Again, I am not positing that their theory is correct, only that it is allowable and yet to be determined rather than obviously wrong.

 

[jal]

Good find.
Here is another.
http://imagine.gsfc.nasa.gov/docs/ask_astro/answers/970408c.html
Ask an Astrophysicist
" So, in the basic definition of a black hole I used above (where the size of the object is smaller than the Schwarzschild radius) the whole Universe is one big black hole with us on the inside.

Therefore, the simple answer is that we are inside the event horizon of the whole Universe, and there is no way that we can escape the Universe's grasp. "
--------
jal