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

[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

 

[jmcgrady]

The theory sounds like Humphrey's "White Hole" with the Milky way at the centre of a bound finite spherical universe.

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

What if an inherent property of the expanding spacetime hosting the dustball counters the effect of gravity? The expansion of space itself ensures that gravity would not prevail.

 

[jal]

I've been waiting for someone to come up with some math so that we would have something concrete to discuss.

WELL!
Sombody has done the calculations!
Some very interesting results are coming out of this approach.
----------
http://arxiv.org/abs/astro-ph/0606448
Concerning the instantaneous mass and the extent of an expanding universe
Authors: H.J. Fahr, Michael Heyl
(Submitted on 19 Jun 2006 (v1), last revised 4 Dec 2006 (this version, v2))
This radius on the other hand can be shown to be nearly equal to the Schwarzschild radius of the so-defined mass of the universe.
--------

jal

 

[jal]

Since everyone is try to get a better understanding of the universe, I assume that you have extended your search and found the following papers.

http://usparc.ihep.su/spires/find/hep/www?rawcmd=a+Heyl,+Michael

----------------
http://arxiv.org/abs/astro-ph/0606048
About universes with scale-related total masses and their abolition of presently outstanding cosmological problems
Authors: H.J. Fahr, M. Heyl
(Submitted on 2 Jun 2006 (v1), last revised 4 Dec 2006 (this version, v2))
Cosmological consequences of a strictly valid total energy conservation for the whole universe are investigated in this paper.
… one can also conclude that for some reason about 70% of the total energy permanently remains in the vacuum during the expansion of the universe - representing itself as vacuum energy - while about 30% manifest itself as matter. This ratio must be constant during the whole evolution of the universe because
both, vacuum energy and matter density, follow the assumed R^−2u scaling.
------------
Cosmic vacuum energy decay and creation of cosmic matter.
Hans-Jörg Fahr, Michael Heyl
Argelander Institute for Astronomy, University of Bonn, 53121, Bonn, Germany, hfahr@astro.uni-bonn.de.
Source: Naturwissenschaften, Volume 94, Number 9, September 2007 , pp. 709-724(16)
Publisher: Springer
Abstract:
In the more recent literature on cosmological evolutions of the universe, the cosmic vacuum energy has become a nonrenouncable ingredient. The cosmological constant Λ, first invented by Einstein, but later also rejected by him, presently experiences an astonishing revival. Interestingly enough, it acts like a constant vacuum energy density would also do. Namely, it has an accelerating action on cosmic dynamics, without which, as it appears, presently obtained cosmological data cannot be conciliated with theory. As we are going to show in this review, however, the concept of a constant vacuum energy density is unsatisfactory for very basic reasons because it would claim for a physical reality that acts upon spacetime and matter dynamics without itself being acted upon by spacetime or matter.
---------------
http://arxiv.org/abs/0710.0269v1
Einstein universes stabilized
Authors: Erhard Scholz
(Submitted on 1 Oct 2007)
The hypothesis that gravitational self-binding energy may be the source for the vacuum energy term of cosmology is studied in a Newtonian Ansatz. For spherical spaces the attractive force of gravitation and the negative pressure of the vacuum energy term form a self stabilizing system under very reasonable restrictions for the parameters, among them a characteristic coefficient \beta of self energy. In the Weyl geometric approach to cosmological redshift, Einstein-Weyl universes with observational restrictions of the curvature parameters are dynamically stable, if \beta is about 40 % smaller than in the exact Newton Ansatz or if the space geometry is elliptical.
========
jal

 

[jal]

I would presume that the Mach's Principle was understood by : R. G. Vishwakarma, and Parampreet Singh when they wrote the following paper and equated the brane to the Schwarzschild horizon and proposed various answers.
http://lanl.arxiv.org/abs/astro-ph/0211285v3
Can brane cosmology with a vanishing \Lambda explain the observations?
Authors: R. G. Vishwakarma (IUCAA), Parampreet Singh (IUCAA)
(Submitted on 13 Nov 2002 (v1), last revised 21 Mar 2003 (this version, v3))

In brane cosmology, the homogeneous, isotropic RobertsonWalker (RW) universe can be envisioned as a hyper surface embedded in the Schwarzschild anti-deSitter (AdS) bulk spacetime.

The small fluctuations (anisotropies) in the temperature of CMB offer a glimpse of the epoch in the early universe when photons decoupled from the cosmic plasma at zdec = 1100. Before this epoch, matter and radiation were tightly coupled and behaved like a single fluid. (insert comment – a quark-gluon liquid).
At z = 1100, the temperature dropped sufficiently to let the protons capture electrons to form neutral hydrogen and other light elements (recombination). . (insert comment – prior to z = 1100, Hydrogen was a solid then a liquid then a gas).
As the electrons, which had trapped photons, disappeared reducing the opacity for Thomson scattering, the photons decoupled (last scattered) from matter.

The initial fluctuations in the tightly coupled baryon-photon plasma oscillate at the speed of sound driven by gravity, inertia of baryons and pressure from photons. This continues until the recombination epoch. Physically these oscillations represent the hot and cold spots on the fluid generated by compression and rarefaction by a standing sound or acoustic wave. Thus the wave which has a density maximum at the time of last scattering, corresponds to a peak in the power spectrum.
The locations of the peaks are set by the acoustic scale ℓA, which can be interpreted as the angle subtended by the sound horizon at the last scattering surface. This angle (say, θA) is given by the ratio of sound horizon to the distance (angular diameter distance) of the last scattering surface:

 

[jal]

A politically correct was of using a black hole horizon = "future event horizon".

http://xxx.lanl.gov/abs/astro-ph/0601598
Dynamical dark energy with a constant vacuum energy density
Authors: B. Guberina, R. Horvat, H. Nikolic
(Submitted on 26 Jan 2006 (v1), last revised 20 Mar 2006 (this version, v2))
A symmetry principle of gravitational holography [1] serves as a window to a complete
theory of quantum gravity. According to that principle, the description of a physical system shows equivalence between a theory having the gravitational field quantized and a theory defined on the boundary encompassing a system whose dimension is lower by one.

We start with the fact that in an ever accelerating universe there always exists a future event horizon. Thus, analogously to the black-hole horizon, it can be attributed some thermodynamical quantities, like entropy and temperature.

The GSL states that the entropy of the event horizon plus the entropy of matter and radiation in the volume within the horizon cannot decrease in time.
======
I hope that I've presented enough info for even the hardest skeptic.
Jal

 

[jal]

The following approach is relevant to this thread.
http://arxiv.org/abs/0804.1771
The cosmic variance of Omega
Authors: T. P. Waterhouse, J. P. Zibin
(Submitted on 10 Apr 2008)

 

[jal]

http://arxiv.org/abs/hep-th/0603133
Naturalness of the Vacuum Energy in Holographic Theories
Authors: Csaba Balazs, Istvan Szapudi
(Submitted on 17 Mar 2006)
Based on the cosmic holographic conjecture of Fischler and Susskind, we point out that the average energy density of the universe is bound from above by its entropy limit. Since Friedmann's equation saturates this relation, the measured value of the cosmological energy density is completely natural in the framework of holographic thermodynamics: vacuum energy density fills the available quantum degrees of freedom allowed by the holographic bound. This is in strong contrast with traditional quantum field theories where, since no similar bound applies, the natural value of the vacuum energy is expected to be 123 orders of magnitude higher than the holographic value. Based on our simple calculation, holographic thermodynamics, and consequently any future holographic quantum (gravity) theory, resolves the vacuum energy puzzle.

 

[foolosophy]

If we are in fact living in a black hole then te BLACK HOLES we are describing within our own reality arent really balck holes but something else entirely.

You have set up a convoluted argument - close to a mathematical paradox by posing the question in that way.

And in any case there is no way of knowing.

A few points though come to mind -

If we are indeed living in a black hole, then why is it expanding?

Why are we proposing a BIG BANG cosmological model?

Why arent we detecting any material or energy that should be entering our little black hole via the event horizon?

What exactly is the Cosmic Backgound radiation then?

 

[jal]

My quest started by a simple question, “How is the universe made and how does it works?”
As you can see in my blog, many have asked this question and there are many different approaches to try to get an answer.
I get my pleasure from seeking the answers.
I have not found the answer but I’m still looking.
jal

 

[foolosophy]

The Socratic Method

The Socratic method is over 2500 years old and involves the gaining of wisdom and knowledge via the asking of questions - its still a fundamental basis for education and teaching throughout the world today.

 

[foolosophy]

confusing the location of the event horizon with the actual singularity itself is a common miss interpretation of what a Black hole is.

 

[jmcgrady]

...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.

What if the Milky Way was at the centre of the BH? Say the universe is a bounded sphere. And that there is a greater density of galaxies near the centre - so much so that the schwarzschild BH criteria are met some distance from the centre such that the radius is less than 13.7 billion light years but greater than X billion light years. Would this explain why we see most galaxies as red shifted?

 

[jal]

Leonid V. Verozub, will be making a presentation at the NEB-XIII Poster Session http://www.astro.auth.gr/~neb-13/program-posters.pdf
http://www.astro.auth.gr/~neb-13/programme.html
Here is his latest paper.
http://arxiv.org/abs/0805.0313v1
On accelerated Universe expansion
Authors: Leonid V. Verozub
(Submitted on 2 May 2008)
Abstract: It is shown that observed peculiarities of the Universe expansion are an inevitable consequence of the gravitational force properties following from gauge-invariant gravitation equations considered in detail in an author's paper in Annalen der Physik, v.17, 28 (2008).

 

[jonmtkisco]

Hi Jal,

Do you know if it's possible to get the Verozub paper from Ann. Phys. (Berlin) 2008? Apparently that's where he describes his underlying equations.

His solution for gravitational acceleration changing sign at a large distance and then declining to zero at infinity sounds like a good conceptual match for a kinematic-GR model. Then gravity can be the source of all kinematics in the universe.

At least it's worth understanding in more detail.

Jon

 

[jal]

I can only access his papers by "clicking" on his name. I did not check out the rest of his papers. Maybe there is something there.
jal

 

[jonmtkisco]

HI jal,

It turns out he has a dozen or so papers on arXiv, all playing around with the same idea. His math is pretty inaccessible.

Jon

 

[yuiop]

...from post#40...

and around big bang time, stuff was WAY denser than Schwarzschild requires, so why didnt the universe collapse then and there? Because it was expanding so fast.
...

Hi Marcus,

I normally hang around in the relativity forum (but I am by no means a relativity expert) and while playing around with Schwarzschild solutions I made a discovery that I think is very relevant to this thread and may provide an alternative answer to the question you pose here.

The equation for coordinate acceleration in the exterior Schwarzschild solution is:

$$a '=\frac{GM}{R^2}\left(1-\frac{R_s}{R}\right)$$

When R is greater than the Schwarzschild radius the gravitational acceleration is positive towards the mass as you would expect. When R is less than the Schwarzschild radius the gravityational acceleration is negative and directed outwards towards the event horizon. if for example all the mass of the universe was originally confined to radius of R=Rs/10 then the outward acceleration is -900 GM/Rs^2. If the mass was confined to R=Rs/1,000 then the outward acceleration is -999,000,000 GM/Rs^2. Obviously, the outward gravitational acceleration gets considerably larger as original density increases.

Now if we look at the coordinate velocity of photon falling from infinity the equation is:

$$c '= c\left(1-\frac{R_s }{R}\right)$$

and for R>Rs the coordinate velocity is always less than c, the velocity of light at infinity. Below the Schwarzschild radius the coordinate velocity of light get larger than c and is negative. This value for R<Rs is the speed of light falling from the centre outwards towards the event horizon. So for a universe with an extreme initial density photons (and particles with mass) move outwards towards the Schwarzschild radius at velocities much greater than c. In other words the outward expansion would very rapid until the universe reached the size of its own Schwarzschild radius. In fact the expansion would be arbitarily high and only limited by the initial density. The greater the initial density the greater the initial expansion. This would be very like the inflation that is thought to have occurred early in the history of the universe. For falling particles the coordinate velocity is given by:

$$v ' = c\sqrt{{Rs \over R}} \left(1-\frac{R_s}{R} \right)$$

One possible objection to this idea is that the coordinate velocity of the outward moving particles becomes zero at the Schwarzschild radius bring everything to a stop. I think this issue can be resolved by considering a universe with an initially flat spacetime. The rapid expansion of the particles within the Schwarzschild volume sends a gravitational shock wave that ripples outwards. Gravity waves have no difficulty passing event horizons and carry energy away with them. The loss of energy from the Schwarzschild volume reduces the Schwarzschild radius, releasing the particles trapped at the event horizon. The process is self destructive and the event horizon dissappears.

If dark energy is ignored this model would basically oscillate, with the universe expanding and collapsing to point and then expanding again. With dark energy it may never collapse.

I came to this conclusion while investigating the interior Schwarzschild solution that enables you examine what happens to a black hole as it forms and found that normal stable black holes do not have a singularity of infinite density at the centre but are a thin shell of matter just outside the event horizon.


For more equations and background on these ideas, see these threads:

https://www.physicsforums.com/showthread.php?t=238839&page=2 post #19 onwards.

https://www.physicsforums.com/showpost.php?p=1767802&postcount=17

https://www.physicsforums.com/showthread.php?t=223730&page=2 post#19

I hope these ideas are of interest. The nice thing about them is that they basically fall straight out of the Schwarzschild solutions. I am not saying dark energy does not exist or that the Schwarzschild solutions might have to be modified a bit to allow for expanding spacetime, but I am saying that that even without those things the Schwarzschild equations do not imply the universe would be trapped in a black hole even when there technically enough mass within a given radius to be a black hole. In fact, examination of the solutions show the universe would be very different if we were inside a black hole.

 

[yuiop]

One possible objection to this idea is that the coordinate velocity of the outward moving particles becomes zero at the Schwarzschild radius bring everything to a stop. I think this issue can be resolved by considering a universe with an initially flat spacetime. The rapid expansion of the particles within the Schwarzschild volume sends a gravitational shock wave that ripples outwards. Gravity waves have no difficulty passing event horizons and carry energy away with them. The loss of energy from the Schwarzschild volume reduces the Schwarzschild radius, releasing the particles trapped at the event horizon. The process is self destructive and the event horizon dissappears.

I just found a counter argument to my above statement. Damn!
http://en.wikipedia.org/wiki/Birkhoff's_theorem_(relativity )

Birkhoff's theorem states a pulsating spherical mass can not give off gravitational waves. That seems reasonable as the gravitaional filed of a sperical object always looks like a point source outside the mass of the body.

There are however any number of potential ways that the mass trapped in a shell at the Schwarzschild radius can escape. The loss of a single atom or photon by Hawking radiation or quantum tunelling would start the destruction of the event horizon. This is even more likely as there is no CMB radiation adding to the mass/energy of the Schwarzschild mass at this epoch. The other method is to observe that the escape velocity at the event horizon is c and that during the inflation period the velocities of exceed c as explained in my last post.

So for those who cherish the notion that if the universe is expanding, that it must have been smaller and denser at some time in the past, GR can cope with that. For those that don't like that notion, you can take comfort with thought of a universe that started infinite in volume and mass and then continued expanding.