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

[marcus]

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

What I am wondering is WHO HERE THINKS WE ARE IN A SCHWARZSCHILD BLACK HOLE where the black hole event horizon coincides with one of the two well-known cosmology horizons?

There are a couple of well-known horizon radii that we hear about a bunch:

the Hubble radius
this is c/H₀ and is the distance at which normal recession speed is c.
If I remember right, something around 13.5 billion LY, current distance.
(the radius of the Hubble sphere, as sometimes called)

the radius of the cosmological event horizon
In past years we've discussed this at PF quite a lot. I recall reading about it in Lineweaver's excellent 2003 paper, where one of the figures shows it as around 16 billion LY. Events that occur today outside the cosmological event horizon cannot ever affect us.
We are out of causal contact with current events at that distance---ASSUMING the LCDM model with its constant positive Lambda.

If Lambda is really zero and the present small positive measured value is an artifact, then the cosmological event horizon would not exist---events that occur today at arbitrarily large distances could eventually affect us, light from them could eventually reach us etc. But the LCDM model has this interesting feature (which Lineweaver 2003 presents in a nice clear treatment.)

I guess either radius could be called a "cosmic horizon" although this runs a risk of confusion because it wouldn't necessarily be clear which of the two was meant.
There were a couple of recent papers by Melia where he used that term. My impression was that he means the Hubble radius, but I could be wrong.

Anyway, I get the impression that some people think the universe inside one of these horizons is a Schwarzschild black hole and that the horizon, whichever one is meant, is the BLACK HOLE EVENT HORIZON of the black hole that we are in. This never occurred to me to imagine, and it simply does not make sense to me. But because similar WORDS are used I guess people can get the idea. Or maybe there is more to it, that I don't understand!

So here's the poll. Are we in a black hole?

 

[marcus]

Well Chris for goodness sake please register a "No" on the poll
We actually have people here at PF who think Yes, and the poll got a yes vote within 1 minute of being posted.

 

[jal]

I voted yes! ... Even though it goes against what I have learned.
The theoretical work implies it. The observations of some papers are inclined to say yes.
In fact http://arxiv.org/abs/0711.4810
Dark Energy in Light of the Cosmic Horizon
Authors: Fulvio Melia
(Submitted on 29 Nov 2007)
Says that we cannot tell. YET...
It must be worth while not to reject the model.
Sooooo, how is an amateur able to decide?
jal

 

[jal]

If I would not be studying the papers, I would not be able to answer.

 

[patty144]

Hi all. I wrote to Prof. Melia over the weekend about this very issue, and this is what he wrote:

Hi Patti:

thanks for writing. I don't mind at all. I may not always be able to
answer right away, but I try to get to all of my e-mail, so do feel
free to write whenever...

Yes, the Cosmic Horizon is not very difficult to understand, nor why
it arises in the first place. It helps if you know electrodynamics,
because this effect is similar (though not the same!) as what one
encounters there.

If you have a uniform, infinite (or effectively infinite) medium,
then if you cut out a spherical cavity in that medium, there is
absolutely no gravitational field/acceleration within the cavity.
The symmetry provides a perfect cancellation of the field created
by all of the sources outside of the cavity.

Thus, if you now place a mass, say an apple, at the center of that
cavity, then the gravitational field (or curvature, if you prefer
to think in those terms) produced by that apple inside the cavity
is as if there were nothing else outside---as if the apple were
the only source in the whole universe.

Now imagine gradually filling the cavity while you move out
to larger radii. Eventually, you reach the radius at which the
enclosed mass produces a Schwarzschild surface there.

Using the term "black hole" is not appropriate here because a
black hole, as we define it, is an object surrounded by vacuum.
But what is true is that light signals reaching us at the origin
of our coordinates from that radius, let's now call it the cosmic
horizon, are infinitely redshifted.

Does that mean there's nothing "on the other side"? No, of course
not. The universe is probably infinite. But any light that would
be approaching us from beyond the Cosmic Horizon is infinitely
redshifted, and therefore carries no signal or information.

Please note that this does not mean we live inside a black hole.
It's important to get that straight, because that term has come
to mean something else. But it does mean that our Cosmic Horizon
is as far as we can ever get information from events occurring
in our realizable universe. Whatever happens outside is not
communicable to us.

Also, please note that this Cosmic Horizon is not necessarily
static. It is only fixed for all time in a so-called de Sitter
universe, because in such a universe the density does not change,
so the horizon radius itself does not change. In a more realistic
universe, containing matter and radiation, as well as possibly
a vacuum energy density, this radius changes. In fact, it increases
with time. So as the universe ages, we get to see more and more
of it.

But this too must end, if the universe contains a cosmological
constant. In that case, eventually matter and radiation wither
away to zero, while the vacuum energy stays constant forever.
So our future would then be in a de Sitter universe, and the
Cosmic Horizon would then approach the de Sitter limit and
stay fixed at that value forever thereafter.

Best wishes,
Fulvio======================================================
Newly Released: "The Galactic Supermassive Black Hole"
http://press.princeton.edu/titles/8453.html

Fulvio Melia
The University of Arizona
Department of Physics & Steward Observatory
Rm 447, PAS #81 (520) 621-9651
http://www.physics.arizona.edu/~melia
======================================================

 

[marcus]

Thanks Patty, everything he says agrees with my understanding as well.
I think what he calls the "cosmic horizon" is the sphere at Hubble radius and he says it is a "Schwarzschild surface" which does not mean there is a black hole but simply that we don't get info from outside that surface.

so if something is ANALOGOUS to a black hole, it is what is OUTSIDE that spherical surface (our part of the universe is not the analog, it is all the rest that is the analog---and the analogy is very weak)

 

[Wallace]

Thanks Patty, everything he says agrees with my understanding as well.
I think what he calls the "cosmic horizon" is the sphere at Hubble radius and he says it is a "Schwarzschild surface" which does not mean there is a black hole but simply that we don't get info from outside that surface.

I must admit I'm not entirely sure what he means by his use of the term "Schwarzschild surface" in this context? His apple-in-a-cavity thought experiment implies that there is a requirement for some critical amount of enclosed matter for the horizon to appear, but it is not clear how that critical requirement relates to anything from the Schwarzschild Solution. Well, it's not clear to me at this point anyway.

I must admit I still haven't read the first Melia paper in the recent pair that came out, and I'm sure it is explained in more detail in there.

 

[jal]

I must admit I'm not entirely sure what he means by his use of the term "Schwarzschild surface" in this context? His apple-in-a-cavity thought experiment implies that there is a requirement for some critical amount of enclosed matter for the horizon to appear, but it is not clear how that critical requirement relates to anything from the Schwarzschild Solution. Well, it's not clear to me at this point anyway.

I was thought that Schwarzschild radius implied that nothing could get out... it's a "brick wall"... as a result ... anything inside can only bounce around.
It a good way to get conservation of energy... nothing can escape.

 

[George Jones]

Can any stuff here and now escape to future null infinity (scri +)?

 

[cristo]

Can any stuff here and now escape to future null infinity (scri +)?

That depends on the metric that we're taking, doesn't it?

I don't understand the idea proposed by people modelling the universe as schwarzschild: How can there be a global schwarzschild geometry when there is an assortment of matter; i.e. the matter is not confined to one specific location (or centre)?

 

[George Jones]

Can any stuff here and now escape to future null infinity (scri +)?

Do this even make sense?

What does the conformal diagram for our $\Lambda$CDM universe look like?

 

[Wallace]

Do this even make sense?

What does the conformal diagram for our $\Lambda$CDM universe look like?

Check the figures from Davis & Lineweaver. They have a very clear figure or two of the conformal representation of several cosmologies, including LCDM.

 

[jonmtkisco]

Prof Melia's description of a spherical cavity sounds like the result Peebles describes from Birkhoff's theorem. Which is why it's possible to consider any reasonably sized spherical subset of an expanding universe without regard to all of the mass/energy outside the sphere.

Also, as I understand it, the typical density of a black hole is about equal to the density of water. Obviously, our universe currently is far less dense. At some early time it was that dense, but I don't think there's any explanation how a black hole could ever get as un-dense as our observable universe.

 

[chronon]

Too many horizons

There seem to be a lot of candidates for what can be called a cosmic horizon, and it's important not to get them mixed up. (see http://www.chronon.org/Articles/cosmichorzns.html)

1) Hubble Sphere: This has no physical significance whatsoever.

2) Particle horizon: This is the limit of what can have had any effect on us since the big bang. It occurs in most models of the universe which have gravitating matter.

3)Cosmological Event horizon: This occurs when the expansion of the universe is accelerating. It has some similarities to the event horizon of a black hole (see http://www.chronon.org/articles/Cosmological_Event_Horizon.html)

4) Now Melia seems to have invented another horizon, which is the radius at which the matter around us would form a black hole. I'm very suspicious about this, since if you go back in time, this horizon encompasses a smaller and smaller part of the universe, and yet we have somehow got beyond the 'black hole' we were in then. Its interesting to look for what the problem is with Melia's horizon. I would guess that as long as his horizon lies outside the particle horizon, the matter won't be able to form a black hole. If we lived in a closed universe which was destined to recollapse to a singularity then it might be reasonable to say that we were in a black hole.

Hopefully Chris Hillman will be along in a short while to set us straight on this matter.

 

[George Jones]

Check the figures from Davis & Lineweaver. They have a very clear figure or two of the conformal representation of several cosmologies, including LCDM.

I have somehow misplaced :grumpy: my hardcopy of this article, but looking online last night, I didn't see what I was looking for. Now, I have roughly the same spacetime coordinates as my books, so I have looked in Hawking and Ellis, which has a conformal diagram for de Sitter spacetime, and, in the future, our $\Lambda$CDM spacetime looks like this, i.e., future null infinity is spacelike. In the past, however, $\Lambda$CDM has a Big Bang singularity.

Here's what I was hinting at.

For a spacetime M, define a black hole to be the region B = M - J^-(scri^+). Here scri^+ is future null infinity and J^- denotes causal past. A particle (photons included) at any event p in B cannot escape to infinity, since p isn't in the past of infinity.

For our $\Lambda$CDM spacetime, which seems to model observations well, everything is in the past of future null infinity, so B is empty; our $\Lambda$CDM spacetime is not a black hole spacetime.

(No, I'm not saying that black holes don't exist in our universe.)

While there are lots of horizons, including event horizons for particles (since future null infinity is spacelike), none of these is a black hole event horizon, since the boundary of the (causal) past of future null infinity is empty.

 

[Vast]

I chose no, because the dynamics of a BH horizon and the cosmological event horizon seem to behave very differently.

But then again I could be wrong.

 

[jal]

A review by Ruth Gregory. A theoretical physicist at Durham University, UK

http://wwwphy.princeton.edu/~steinh/
Paul J. Steinhardt
Endless Universe: Beyond the Big Bang
Paul J Steinhardt and Neil Turok

Inflation was designed to solve some problems which can also be solved by the cyclic universe.
Steinhardt and Turok the universe is simply a slice (known as a brane) through these extra dimensions, and the Big Bang was a collision of branes — a huge cosmic thunderclap. This model builds on an idea called M-theory, in which the strings live on two walls at the end of an 11D space–time. Applying the usual rules of string theory leads to a general picture in which these walls can move across the canyon separating them, and occasionally (every trillion years or so according to Steinhardt and Turok) slam into each other. It is this slamming together that is responsible for what we see as the Big Bang, although from a higher-dimensional point of view it is a collision rather than a singularity.

One message the authors communicate clearly is that we should never accept something simply because most people say it is true, but should constantly challenge and look for alternatives to any picture that cannot be rigorously proven.
--------
present vote …
yes, … 2
no, … 12
-------
hehehe :rofl:

 

[jal]

If you have been reading the papers then it is obvious that The Cosmic Horizon
by Fulvio Melia has got as much observational info for it to be considered a serious candidate as any other model.
If you support colliding branes then they would create a Cosmic Horizon. There is no reason to assume that our universe was the only one created by colliding branes. Therefore, the logic would be to assume that the “bulk” or “cosmos" is populated with 10^500 universes each having their own Cosmic Horizon. All would be irrelevant … until … they meet and mearged.

 

[pervect]

While the majority of the posters have already gotten the right answer (no), some of the answers were quite technical.

I would like to point out that this question is addressed in less technical terms in the sci.physics.faq Is the Big Bang a black hole?

What is the distinction between the big bang model and a black hole?

The standard big bang models are the Friedmann-Robertson-Walker (FRW) solutions of the gravitational field equations of general relativity. These can describe open or closed universes. All these FRW universes have a singularity at the origin of time which represents the big bang. Black holes also have singularities. Furthermore, in the case of a closed universe no light can escape which is just the common definition of a black hole. So what is the difference?

The first clear difference is that the big bang singularity of the FRW models lies in the past of all events in the universe, whereas the singularity of a black hole lies in the future. The big bang is therefore more like a white hole which is the time reversal of a black hole. According to classical general relativity white holes should not exist since they cannot be created for the same (time-reversed) reasons that black holes cannot be destroyed. This might not apply if they always existed.

But the standard FRW big bang models are also different from a white hole. A white hole has an event horizon which is the reverse of a black hole event horizon. Nothing can pass into this horizon just as nothing can escape from a black hole horizon. Roughly speaking, this is the definition of a white hole. Notice that it would have been easy to show that the FRW model is different from a standard black or white hole solution such as the static Schwarzschild solutions or rotation Kerr solutions, but it is more difficult to demonstrate the difference from a more general black or white hole. The real difference is that the FRW models do not have the same type of event horizon as a white or black hole. Outside a white hole event horizon there are world lines which can be traced back into the past indefinitely without ever meeting the white hole singularity whereas in a FRW cosmology all worldline originate at the singularity.
Could the big bang be a black or white hole all the same?

In the previous answer I was careful to only argue that the standard FRW big bang model is distinct from a black or white hole. The real universe may be different from the FRW universe so can we rule out the possibility that it is a black or white hole?

The short version is that the big bang is definitely not a black hole. The question "Is the big bang a white hole" is more interesting, and the FAQ talks about this in more depth than the section I quoted above, but while this is IMO a more interesting question, it is not what was asked and I don't want to derail the thread.

 

[hellfire]

Of course the FRW solution is not the Schwarzschild solution. Prof. Baez answer seems to me like 'both solutions are not the same because they are two different solutions'. To my eyes the interesting question is rather how could the experimental data fit to such a proposal.

The best agreement with all the cosmological experimental data is provided by the standard model of cosmology. However, it could be a pedagogic exercise to try to figure out how to explain some basic facts assuming a Schwarzschild geometry. For example, is it possible to have redshift, time dilation and variations of brightness according to data in a Schwarzschild solution? If yes, with what constraints or conditions? What then about other cosmological tests such as the CMB or the ratios of light elements?

 

[George Jones]

Of course the FRW solution is not the Schwarzschild solution. Prof. Baez answer seems to me like 'both solutions are not the same because they are two different solutions'.

This is the tack that I, too, took in my posts.

To my eyes the interesting question is rather how could the experimental data fit to such a proposal.

I've been wondering when someone would say this.

The best agreement with all the cosmological experimental data is provided by the standard model of cosmology. However, it could be a pedagogic exercise to try to figure out how to explain some basic facts assuming a Schwarzschild geometry. For example, is it possible to have redshift, time dilation and variations of brightness according to data in a Schwarzschild solution? If yes, with what constraints or conditions? What then about other cosmological tests such as the CMB or the ratios of light elements?

I suspect that the answers to some (many?) are no, but it would be nice to see the answers (yes or no) worked out for extended Schwarzschild, and deep inside extended Kerr (without Poisson/Israel).

 

[jal]

It appears that Fulvio Melia does not have to worry about "the inquisitors". Let the data speak. (pedagogic exercise?)
jal

 

[lightbeing]

yes

If proven to exist (you make the call i guess) it would facilitate a necessity to be true that indeed we are. Also, if this the case, only a shallow outlook would consider the obverse. xlated--> Meaning short sighted realization or an overlooking based on what resolute level you have modeled the obsrevation upon.

 

[jonmtkisco]

To my eyes the interesting question is rather how could the experimental data fit to such a proposal.

... However, it could be a pedagogic exercise to try to figure out how to explain some basic facts assuming a Schwarzschild geometry.

This exercise sounds suspiciously like Arthur Eddington's (supposedly tongue-in-cheek) proposition in the 1930's that the universe is not expanding, instead all of the matter is shrinking. Such a theory can easily explain redshift (shrinking measuring rods of the observer), but messes up all sorts of other things, such as the speed of light and quantum mechanics.

Jon

 

[jal]

I think that the "thought of "edge" is the scarry part.
Depending on who you talk to there are different "edge".
Here is a partial list commencing by the most accepted.
1. Infinite -- no edge
2. Light cone --- speed of light
3. Hubble --- Expansion size
4. Cosmic Horizon/white hole/black hole/schwartchild radius --- gravity (this discussion)
5. dimensions --- 3d ---> more dimensions
6. multi-universes, --- vacuum energy ---> 10^500 bubble universes
---------
Here is some interesting reading
http://en.wikipedia.org/wiki/Brans-Dicke_theory
In theoretical physics, the Brans-Dicke theory of gravitation (sometimes called the Jordan-Brans-Dicke theory) is a theoretical framework to explain gravitation. It is a well-known competitor of Einstein's more popular theory of general relativity. It is an example of a scalar-tensor theory, a gravitational theory in which the gravitational interaction is mediated by a scalar field as well as the tensor field of general relativity.
-----------
http://en.wikipedia.org/wiki/Self-creation_cosmology
Self-creation cosmology (SCC) theories are gravitational theories in which the mass of the universe is created out of its self-contained gravitational and scalar fields, as opposed to the theory of continuous creation cosmology or the steady state theory which depend on an extra 'creation' field.
As an alternative gravitational theory SCC is a non-standard cosmology in which the Brans-Dicke theory (BD) has been modified to allow for mass creation. It relaxes the requirement of the conservation of energy-momentum (or four-momentum) so the scalar field may interact directly with matter.

 

[Garth]

---------
Here is some interesting reading
-----------
http://en.wikipedia.org/wiki/Self-creation_cosmology
Self-creation cosmology (SCC) theories are gravitational theories in which the mass of the universe is created out of its self-contained gravitational and scalar fields, as opposed to the theory of continuous creation cosmology or the steady state theory which depend on an extra 'creation' field.
As an alternative gravitational theory SCC is a non-standard cosmology in which the Brans-Dicke theory (BD) has been modified to allow for mass creation. It relaxes the requirement of the conservation of energy-momentum (or four-momentum) so the scalar field may interact directly with matter.

Cough, cough.

If you read further on under "Falsifiable tests of the theory" you will find the statement:

One of them, the Gravity Probe B geodetic precession, which measures the precessions of four accurate orbiting gyroscopes, is being evaluated in 2007; SCC predicts 2/3 that of the GR N-S precession, i.e. 4.4096 arcsec/yr. whereas the frame-dragging or gravitomagnetic E-W precession prediction is the same as that of GR i.e. 0.0409 arcsec/yr. The first results of this experiment were published at the American Physical Society Meeting on the 14th April 2007. While unforeseen errors are still being determined through 2007 the geodetic precession measurement of 6.6 arcsec/yr, which is within 1% of the GR prediction, is fatal to the present form of SCC.

A general version of the theory in which $\lambda \ne 1$ is being prepared, watch this space...

You may also be interested in the latest posts to the thread Alternative theories being tested by Gravity Probe B...

That http://einstein.stanford.edu/cgi-bin/highlights/showpic.cgi?name=GR-85-day_result.jpg is showing that to a 1 sigma error confidence level the results for the geodetic precession are inconsistent with GR.

This is at about a 68% confidence level, we wait for the 3$\sigma$ 4-gyro results next year, but so far it does look interesting!

Garth

 

[Garth]

You may also be interested in the latest posts to the thread Alternative theories being tested by Gravity Probe B...

That diagram is showing that to a 1 sigma error confidence level the results for the geodetic precession are inconsistent with GR.

This is at about a 68% confidence level, we wait for the 3LaTeX graphic is being generated. Reload this page in a moment. 4-gyro results next year, but so far it does look interesting![

Now that is interesting, the GP-B website has withdrawn that diagram and replaced it with one that makes no such claims!

Garth

 

[Chronos]

Of course you can manipulate all the necessary variables to create a 'universe' that looks like the inside of a black hole. The exercise is, however, meaningless. You can also model the universe as a hydrogen atom - an equally meaningless, but amusing proposition.

 

[jal]

Is the bounce approach meaningless, in your opinion?
If not... once the 10^80 particles have been "made" ... how do you remove the gravity so that you can start the next phase wthout having a cosmic horizon already in place.

 

[marcus]

Of course you can manipulate all the necessary variables to create a 'universe' that looks like the inside of a black hole. The exercise is, however, meaningless...

I agree it would be meaningless. And I wouldn't know how to manipulate variables so as to even fake it---if the aim is to get an expanding universe (expanding at infinity). Because the Schw. solution (on which basis things like the Schw. radius and event horizon are defined) is a STATIC solution. the geometry does not change. In Schw. model, outside space is not expanding.

To illustrate, near the "bigbang" onset of expansion you don't have a static solution, you have a dynamic solution to EFE which is expanding so fast that essentially it doesn't matter how many matter particles you have briefly packed into how small a space, you still don't get a black hole (even at density approaching Planck!).

I don't see how there can be a difference of opinion. Even Fulvio Melia says clearly and emphatically that we are not in the interior of a black hole. And he is not a cosmologist---he does observational astrophysics and writes popularization books, if I recall correctly---so he could be forgiven if he used some terminology in an unconventional way that would give a naive reader the wrong idea. Cosmology is not his field. But he is definite (see Patty's letter) about our not being inside a black hole.
Experts please correct me if I'm mistaken but in my experience the Schwarzschild radius formula 2GM/c^2 can come up in other contexts to give other distances, and in the black hole situation it does NOT GIVE THE DISTANCE FROM THE central singularity out to the event horizon as an observer inside the event horizon would likely measure it. If we were actually inside a black hole of mass M, we would NOT estimate the distance to the event horizon as 2GM/c^2. I wouldn't anyway! What the formula gives is half the diameter of the event horizon as measured by an outside observer, or the circumference divided by 2pi. It does not give the radius as a person inside would be apt to see it (poor guy!).

So the fact that this same formula happens to come up defining a certain distance from our galaxy out to a certain kind of Melia horizon does in no way indicate that we are in the interior of a black hole. If we were in the interior of a black hole things would look very very very different from what we see. It totally doesn't fit the observational data. Particularly if we were near the CENTER of the spherical horizon, as we are in Fulvio Melia's picture.

Picture it. We'd be at the frikkin singularity!

So Melia doesn't say it and no competent cosmologist says it, and a moment's visualization---if you think visually---makes it obvious that it can't be. I'm puzzled as to how there can be any difference of opinion about this. But thanks to everybody who responded!

Hey, we have 24 responses!
I was curious what other people thought and it's great to have so many responses!
Thanks again, all.

 

[jal]

Let's see if there is a "math kid" who can extrapolate the following to the cosmic horizon.
http://arxiv.org/abs/0712.0817
Loop quantization of spherically symmetric midi-superspaces : the interior problem
Authors: Miguel Campiglia, Rodolfo Gambini, Jorge Pullin
(Submitted on 5 Dec 2007)
------
The above was brought to our attention by marcus
--------
jal

 

[PaulR]

This is my first post but I feel strongly that we are in a BH from the perspective of an "outsider".

First - consider the density of a black hole = Mass/ Volume = 3 * C* C/ (8* G*π * R*R)
Using A value for R = 13.7 billion Light Years gives a density = 9.57 E -24 g/ m^3, which is about the actual density measured today.

Thus it would seem that an "outside" observer measuring our observable universe would see something that has the density of a 13.7 billion light year black hole. Surely that is what is meant by saying we live in a BH.

Now consider someone inside this space with this density and radius..

I do not understand why at this density there should be a singularity at the center. By analogy, the gravity at the center of the Earth cancels out to 0. It does not go up. The same way, the gravity as you move away from the "edge" of a truly massive BH that does not have to fight matter degeneration should drop, not increase.

Thus it does not violate any rules to consider a black hole with that low a density staying low in density all over rather than having a high density in the center.

Second - Look at the relation to the concept that space curvature in our BH is equal 0.

The equation for Density to get 0 curvature is 3 * H * H / 8 * π * G

If you set the two densities equal, you get

3 * H * H / 8 * π * G = 3 * C* C/ (8* G*π * R*R)

This reduces to H = C/R, providing a value for the Hubble constant of 71.373 km/ sec/ Mpc

This is within the estimated value. Doesn't this prediction of the Hubble Constant value provide some validity to this approach? As Hubble measurements get more precise and they converge on this value, would that not prove the likelihood of this conjecture?

It would be an amazing coincidence that the Hubble Constant is the value from the Schwartzild density at the current age of the universe and the observed flatness.

Surely the almost perfect relation between these three is more than coincidence.

As an aside, don't forget the Hawking Radiation that would be occurring if this is a black hole.

 

[jal]

Hi PaulR!
Welcome!
I tried to do the calculations and kept getting my units and zeros mixed up. I'm sure that someone will check your calculations since you came up with a very interesting observation.

It would be an amazing coincidence that the Hubble Constant is the value from the Schwartzild density at the current age of the universe and the observed flatness.

As you know, the Hawking Radiation is related to the size of a black hole. The smaller the the black hole the more radiation/evaporation. Therefore, using the 17 BLY of Fulvio Melia, I would expect no observable radiation/evaporation.
Can someone do a this calculation?

 

[pervect]

Of course the FRW solution is not the Schwarzschild solution. Prof. Baez answer seems to me like 'both solutions are not the same because they are two different solutions'. To my eyes the interesting question is rather how could the experimental data fit to such a proposal.

The best agreement with all the cosmological experimental data is provided by the standard model of cosmology. However, it could be a pedagogic exercise to try to figure out how to explain some basic facts assuming a Schwarzschild geometry. For example, is it possible to have redshift, time dilation and variations of brightness according to data in a Schwarzschild solution? If yes, with what constraints or conditions? What then about other cosmological tests such as the CMB or the ratios of light elements?

I thought the FAQ was pretty clear on this point, actually - however, I didn't quote the applicable sections, because I thought this was wandering away from the original question, and I figured that interested people could read the FAQ on this point.

The answer to "is the universe a black hole" is pretty definite - it's no. It has the wrong structure to be a black hole.

While the universe can't be a black hole, a sufficiently large white hole is basically not distinguishable from a FRW cosmology. This makes the question essentially moot. (There *might* be a way to distinguish the two theories if one was willing to wait several billion years. The one thing that the FAQ might be accused of omitting is the fact that there might *not* be any way to distinguish the two theories if there is indeed some sort of cosmological constant, making the question totally moot rather than moot only in practice.)

Could the big bang be a black or white hole all the same?

In the previous answer I was careful to only argue that the standard FRW big bang model is distinct from a black or white hole. The real universe may be different from the FRW universe so can we rule out the possibility that it is a black or white hole? I am not going to enter into such issues as to whether there was actually a singularity and I will assume that general relativity is effectively correct as for as we are concerned here.

The previous argument against the big bang being a black hole still applies. The black hole singularity always lies in the future light cone whereas astronomical observation clearly indicate a hot big bang in the past. The possibility that the big bang is actually a white hole remains.

...

It follows that the time reversal of this model for a collapsing sphere of dust is indistinguishable from the FRW models if the dust sphere is larger than the observable universe. In other words, we cannot rule out the possibility that the universe is a very large white hole. Only by waiting many billions of years until the edge of the sphere comes into view could we know.

 

[chronon]

This reduces to H = C/R, providing a value for the Hubble constant of 71.373 km/ sec/ Mpc

But H=C/R just gives the radius of the Hubble sphere, and we can certainly see beyond that.