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

[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)
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The above was brought to our attention by marcus
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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.

 

[jal]

Let us see if we can reduce the amount of arm waving.
1. Present interpretations starts from a big bang and a singularity. The universe started from nothing and expanded to an infinite size in only 13.7 billion years.
2. Now we change the story and say that the universe started from a minimum size of 24 units, at the big bang and expanded to infinity in only 13.7 billion years.
3. Now we change the story a little bit more and we say that the universe is repeating this contracting and big bang cycle. You are asking that the infinite size of the universe can contract to a size near the Planck scale not only once but repeatedly in a finite amount of time. Tell me, how much finite time do you want to use to have this infinite size universe go through each of these cycles?
4. Now, … let us get real. Let us use a finite size, 17 billion years, of an infinite “cosmo” and see if we get some kind of bouncing universe that correspond to observations. There is only one force, gravity, which will be able to select that finite size so that we can have these repeated cycles of bounce. Therefore, we could imagine that this cosmic horizon could have been smaller in previous bounces and that it grew with the addition of more “matter”. As a result, we are now in a universe that has 10^80 “particles” and it now has a cosmic horizon of 17 billion light years. If you want to eliminate the cosmic horizon then find a way to eliminate the gravity that caused it. If you disagree with a cosmic horizon then you got to find/invent a mechanism that will select a finite size of an infinite universe that will go through the bounce cycles in a finite amount of time.

 

[PaulR]

I apologize but I am confused.
I do not see why having a singularity in the past has any relation to the concept that a sphere of radius 13.7 B light years and a density of the actual current density of our universe would not be a black hole to an observer outside this sphere.
What other charecteristics are needed for a sphere that matches the black hole charecteristics are needed?
How does our 13.7 billion year neighborhood not qualify?
Is there something associated with its past that disqualifies a body from being a black hole?

Wouldn't an outside observer see that light or matter approaching our sphere acts exactly like it would approaching any other black hole? What clue/ measurement would an outside observer have to say this is not a BH?

 

[marcus]

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

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

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

Hi PaulR, welcome to PF! You sound reasonable and able to change your mind.
We are not in a BH with the Hubble Radius as event horizon radius. That would put us at the center and things would look very different.

But if you had a lever that would ABRUPTLY HALT THE EXPANSION OF THE UNIVERSE, like on old train cars there was that rope you could pull in case of emergencies and make it screech to a halt, then we could consider what would happen.

It is a tautology, something built into the algebra, that in the flat case the Hubble radius is given by a formula which looks just like the Schwarzschild radius formula in a VERY DIFFERENT SPACETIME. The Schw. solution to the Einstein equation is a very different spacetime geometry. It is not an expanding Friedmann-LeMaitre. It is not flat inside.
It happens that the same formula gives Schw radius in the very static very unflat case of Schw geometry and also gives the Hubb radius in the very UNstatic very flat case of Friedmann geometry.

Same formula, happens to give two different things in two different geometries.

But suppose you did have an emergency-brake handle that can stop the universe expanding. It is painted red, and has a comfortable grip. You grasp the handle and think... what would happen? It is a serious question because as soon as you pull the universe is going to start collapsing! There is plenty of density for that. All over the place. Many spheres, overlapping ours and much larger, have the required density. The moment you deprive the universe of its expansion it will assume a collapsing geometry.
But that's a different geometry, a different future, a total other kettle of fish.


BTW the Hubble parameter is not constant, even though it used to be called "Hubble constant". And as it changes, the Hubble radius changes. There is no coincidence occurring at this moment of history. What you have noticed is an algebraic fact that is always true. Just not to misinterpret.

 

[PaulR]

Thank you for this explanation.

As a follow up, I have seen many estimates of the Hubble parameter and estimates of the age of the universe.
If the Hubble parameter is algebraically always C/ R, why is this relation not used to refine the estimates.
Instead, the best estimates of H and R are almost but not quite in line with this formula.

It was this lack of assuming they were algebraically related that led me to think they did not have to be related. Then when I saw how close they were I thought that had a significance.

As a second question, does this difference also apply to an expanding black hole? I.e. if a body that has the right density is expanding, does that prevent it from being a black hole.

Finally, what would an observer see when looking at a bubble that is 13.7 b Light years wide with the density we have. How would it differ from a black hole? Would the gravity not be suficient to form an event horizon from this outsider's perspective? Could the outsider easily traverse this sphere back and forth?

 

[marcus]

Thank you for this explanation.

As a follow up, I have seen many estimates of the Hubble parameter and estimates of the age of the universe.
If the Hubble parameter is algebraically always C/ R, why is this relation not used to refine the estimates.
...

You don't specify, but I think by R you mean the HUBBLE RADIUS.
This is the present distance at which a stationary point would now be receding at speed c due to expansion.

One cannot measure this directly---or determine it in any other way than by the usual means for measuring H. So one cannot use measurement of R to refine that of H. It is more the other way around.

What one does is measure H as accurately as possible, sampling recession speed at all convenient distances, then once one has a value for H then one DEFINES the Hubble radius as c/H

(all c/H means is that distance at which the recession speed is c, because H is the ratio of present recession speed to present distance)

As a second question, does this difference also apply to an expanding black hole? I.e. if a body that has the right density is expanding, does that prevent it from being a black hole.

Sure! That is what the people don't understand, who keep talking about us being in black hole. A region of spacetime which is expanding, even if has enough matter density to form hole if it were STATIC, nevertheless if it is expanding fast enough will NOT collapse to hole!

and BTW out at the Hubble radius (that Fulvie Melia was calling "cosmic horizon") stuff is receding at the speed of light so this spacetime region of ours is expanding like a bat out of hell.

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.

Finally, what would an observer see when looking at a bubble that is 13.7 b Light years wide with the density we have. How would it differ from a black hole? Would the gravity not be suficient to form an event horizon from this outsider's perspective? Could the outsider easily traverse this sphere back and forth?

you mean 13.7 billion LY is the Hubble radius, so that is c/H and we are in space that is expanding at the rate H ( equals c/13.7 bLY)
you mean a bubble that has RADIUS equal to that, so it is twice that much wide.

Such a bubble is a typical chunk of our universe. To an outsider out near the bubble surface boundary it wouldn't look any different from any other similar volume. Geometrically it would be approximately flat.
CROSSING any rapidly expanding region raises more complicated issues. But suppose instead of crossing, the outsider just wants to dip in a few million LY and come out again. He could travel in and out of it just as he would venture into any other patch of space.

Remember that even though for us the boundary is receding at speed c, for him out there in the space around the boundary IT IS NOT MOVING. He is IN the space that is receding from us at speed c. So for him it is just ordinary space. there is nothing like a BH event horizon there. There is no point of no return. There is no trap. he can cruise across to our side, and be inside for a while, buy an icecream cone, and then cruise on back to the outside.

 

[PaulR]

Thank you for this clarification

As to R, I was referring to the 13.7 b light years based on the distance light has traveled since the universe began, not the Hubble Radius.
I was noting that one can use the best estimate of the age of the universe to compute the Hubble Parameter, thus providing a different independent estimate of this parameter.
I was wondering why this is not done.

 

[Wallace]

Thank you for this clarification

As to R, I was referring to the 13.7 b light years based on the distance light has traveled since the universe began, not the Hubble Radius.
I was noting that one can use the best estimate of the age of the universe to compute the Hubble Parameter, thus providing a different independent estimate of this parameter.
I was wondering why this is not done.

Because the age calculated from the observed Hubble parameter, so you can't then do it in reverse! We observe H and calculate the age. We can't observe the age of the Universe, though we can put rough lower bounds on it based on other observations, such as the age of globular clusters. There is no current significant 'age problem', since all objects in the Universe are, within the uncertainties, younger than the inferred age from the measured Hubble parameter today and the other cosmological parameters. There are some arguments about how long it would take Black Holes to form in the early Universe as well as some issues with metal abundances at high redshift, but the modelling of these is very uncertain, so it is not a very accurate way of measuring the age from which to calculated H.

 

[marcus]

Thank you for this clarification

As to R, I was referring to the 13.7 b light years based on the distance light has traveled since the universe began, not the Hubble Radius.
I was noting that one can use the best estimate of the age of the universe to compute the Hubble Parameter, thus providing a different independent estimate of this parameter.
I was wondering why this is not done.

the most precise way we estimate the age of the universe is again to first measure H and then use H to compute it.

there are some other ways to estimate the age, like getting statistics on stars and trying to guess how fast different size stars age etc etc. , or studying clusters, or abundances of elements, but those are much rougher and more iffy.

you can use star and cluster statistics and elements and the like as a CHECK on what you get from H, but the main way is to calculate from H.

therefore you cannot use age of universe to refine estimat of H-----it is more the other way around
======================

BTW, you know space is expanding, distances are increasing. You can picture this.
So why do you think that a photon of light would have traveled 13.7 bLY since beginning of expansion?

Don't you imagine it would have covered much much more ground? Because whatever distance it covered during the first part of its trip would have been way stretched out.

But you say

referring to the 13.7 b light years based on the distance light has traveled since the universe began

that can't be right! what do you guess the real figure is?

OOPS, while I was typing this I see that Wallace already replied! Well Paul, now you have two answers. I think I said much the same things as Wallace.

 

[jal]

I am aware of what our present model says:
1. If we look at the CBR we should be seeing light from 10^80 “particles” that were created and existed 400,000 years after the big bang. Protons have not decayed in that time span, therefore, due to expansion, those particles would now be, 47 billion light years away if the Universe is only 14 billion years old.
2. The size of the universe that existed 400,000 years after the big bang would contain all of those 10^80 “particles” and as a result, every direction you looked would eventually end on the surface of a star/particle, and the whole sky would be as bright as the surface of the Sun. This is known as Olbers' Paradox.
3. The numerical value of the CMR redshift is about z = 1089 (z = 0 corresponds to present time). The highest measured quasar redshift is z = 6.4 while as-yet unconfirmed reports from a gravitational lens observed in a distant galaxy cluster may indicate a galaxy with a redshift of z = 10.. There is a big empty hole of knowledge between about z = 1089 and a redshift of z = 10.

There are a lot of particles up to a redshift of z = 10, yet they should be 47 billion light years away according to the present model.
I need a better explanation and I’m willing to examine what Fulvio Melia and others have to say.
===========


http://en.wikipedia.org/wiki/Redshift
The most distant objects exhibit larger redshifts corresponding to the Hubble flow of the universe. The largest observed redshift, corresponding to the greatest distance and furthest back in time, is that of the cosmic microwave background radiation; the numerical value of its redshift is about z = 1089 (z = 0 corresponds to present time), and it shows the state of the Universe about 13.7 billion years ago, and 379,000 years after the initial moments of the Big Bang
Currently, the highest measured quasar redshift is z = 6.4,[46] with the highest confirmed galaxy redshift being z = 7.0[47] while as-yet unconfirmed reports from a gravitational lens observed in a distant galaxy cluster may indicate a galaxy with a redshift of z = 10.
http://www.astro.ucla.edu/~wright/doppler.htm
If the Universe were infinitely old, and infinite in extent, and stars could shine forever, then every direction you looked would eventually end on the surface of a star, and the whole sky would be as bright as the surface of the Sun. This is known as Olbers' Paradox after Heinrich Wilhelm Olbers [1757-1840] who wrote about it in 1823-1826 but it was also discussed earlier. Absorption by interstellar dust does not circumvent this paradox, since dust reradiates whatever radiation it absorbs within a few minutes, which is much less than the age of the Universe. However, the Universe is not infinitely old, and the expansion of the Universe reduces the accumulated energy radiated by distant stars. Either one of these effects acting alone would solve Olbers' Paradox, but they both act at once.
http://www.weburbia.com/physics/olber.html
1. The Universe is expanding, so distant stars are red-shifted into obscurity.
2. The Universe is young. Distant light hasn't even reached us yet.

But the final two possibilities are surely each correct and partly responsible. There are numerical arguments that suggest that the effect of the finite age of the Universe is the larger effect. We live inside a spherical shell of "Observable Universe" which has radius equal to the lifetime of the Universe. Objects more than about 15 billion years old are too far away for their light ever to reach us.
http://www.astro.ucla.edu/~wright/cosmology_faq.html#ct2
If the Universe is only 14 billion years old, how can we see objects that are now 47 billion light years away?
… the most distant object we can see is bigger than 3 times the speed of light times the age of the Universe. The current best fit model which has an accelerating expansion gives a maximum distance we can see of 47 billion light years.
=========

 

[jal]

Fulvio Melia
“We will show that, with the recent WMAP results (Spergel et al. 2003), our observational limit clearly corresponds to the distance beyond which the spacetime curvature prevents any signal from ever reaching us. An observer’s worldline must therefore always be restricted to the region R < R0, i.e., to radii bounded by the cosmic horizon, consistent with the corollary to Birkhoff’s theorem.
The restrictions on an observer’s worldlines should be set by the physical radius R0, beyond which no signal can reach her within a finite time, no matter what internal structure the spacetime may possess.

However, the effects of gravity travel at the speed of light, so what matters in setting the structure of the universe within the horizon at time t is the mass-energy content within R0. The influence of these distant regions of the universe ended once their radius from us exceeded R0.
Our best fit to the Type Ia supernova data indicates that t0 would then have to be ~16.9 billion years. Though surprising at first, an older universe such as this would actually eliminate several other long-standing problems in cosmology, including the (too) early appearance of supermassive black holes (at a redshift > 6) and the glaring deficit of dwarf halos in the local group.
Our study has shown that scaling solutions not only fit the Type Ia supernova data much better than the basic _CDM cosmology, but they apparently simultaneously solve several conundrums with the standard model. As long as the time-averaged value of ! is less than −1/3, they eliminate both the coincidence and flatness problems, possibly even obviating the need for a period of rapid inflation in the early universe (see, e.g., Guth 1981; Linde 1982).
On the observational front, the prospects for confirming or rejecting some of the ideas presented in this paper look very promising indeed.”

--------------
Of course, his approach leads to speculation and other questions which he might have thought of and cannot published …. Yet!
If we can see the light (CBR) 400,000 years after the big bang then that means that those photons (EMF) have not left the universe. The universe was a 400,000 lyr sphere containing all the photons and all the particles. Something had to keep the photons from escaping or otherwise the universe would be losing energy.
It would be like dropping a rock into an ocean. The wave would keep going and never come. So, if there is no barrier, the observed (CBR) cannot be from 400,000 years after the big bang. Those photons are long gone.
Explanation #1
The expansion of the universe is always faster then the speed of light. However, that cannot be right because we would not see the light from other galaxies, gravity would not work, etc.
Explanation #2
As the 400,000 light year sphere of particles expands, at less than the speed of light, the photons (EMF) go faster than the expanding size of the particle sphere but are prevented from escaping and just go bouncing around and around within that barrier.
Therefore, the evidence of the (CMR) is the evidence of a barrier; the conservation of energy is the evidence of a barrier; neutrinos from the big bang epoch are supposed to be still around and if discovered would prove that there is a barrier keeping them here.
--------
What keeps the photons with a redshift of z = 10 to z = 1089 within our universe?
Can anyone do some explanations of red shift of neutrinos? http://conferences.fnal.gov/aspen05/talks/mena.pdf

 

[IMP]

I thought that black holes have maxiumum entropy? Looking around, I see hot areas and cold areas. Also, if we are living inside a huge black hole, how come we actually have black holes? What I mean is: Can there be black holes within black holes?

 

[marcus]

I thought that black holes have maxiumum entropy? Looking around, I see hot areas and cold areas. Also, if we are living inside a huge black hole, how come we actually have black holes? What I mean is: Can there be black holes within black holes?

Sure, black holes can fall into bigger black holes, just like stars and other stuff can fall in
But don't worry about "if we are living inside a huge black hole". Even Fulvio Melia, who keeps getting quoted, has said clearly and explicitly that we are not---his article was not intended to suggest that---he wants it clearly understood, and he says it is important to realize that. Here's part of his recent email message to Patty

Hi Patti:
...
...
Please note that this does not mean we live inside a black hole.
...

Best wishes,
Fulvio

And F. Melia is not an expert in cosmology---his research is in other stuff. Knowing his area of expertise, i certainly would not cite him as an authority on an issue in cosmology like this! But at least he is not so far out of line as to pretend we live in a black hole with event horizon coinciding with something like Hubble sphere or cosmic event horizon (which the poll question was asking).

Personally I doubt his recent paper is publishable as is---will have to be revised to eliminate the possibility that uninformed readers could misinterpret and get the idea he is saying we are in BH.

IMP I see you correctly said "no" on the poll---glad you are not confused about this. I didn't start the thread because it was an open scientific question, that you could reasonably consider either way. As I said at the start, I set up the poll be because I was interested to know if a significant number of people were confused or in doubt.

 

[jal]

There are different levels of readers reading this who have not read the papers or do not understand them.
Therefore, I will do some paraphrasing of what Fulvio Melia has done in his paper.
The picture of the Cosmic Background Radiation is a picture of the universe as it was 400,000 years after the big bang. It is a sphere of 400,000 light years. It contains all of the particles/galaxies (10^80). It contains all of the gravity and all of the photons.
He then shows (with math.) that if you take the known expansion of the universe to NOW, (13.7 billion years), then the particles/galaxies occupy a sphere of 13.7 billion light years. Gravity will occupy a sphere of 16.9 billion light years.
He then concludes that if there are any particles/galaxies outside of that 17 billion light year sphere it can be ignored since it will not have any influence on our universe.
He calls that 17 billion light year sphere the “COSMIC HORIZON”.
He did not go into the specifics of what is happening as the 400,000 light year sphere is expanding. He ends the papers with what he has observed and what he thinks.

Fulvio Melia
Our study has shown that scaling solutions not only fit the Type Ia supernova data much better than the basic _CDM cosmology, but they apparently simultaneously solve several conundrums with the standard model. As long as the time-averaged value of ! is less than −1/3, they eliminate both the coincidence and flatness problems, possibly even obviating the need for a period of rapid inflation in the early universe (see, e.g., Guth 1981; Linde 1982).

The calculation the gravity of the 10^80 particles in the 400,000 light year sphere is left up to the readers to do.

 

[PRyckman]

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)?

What if the point of observation was the center?
Would this help to explain it? Suspend beleif that that is not possible for a moment.

 

[jonmtkisco]

Hi PRyckman,

The Schwarzschild radius solution technically is applicable only in empty (vacuum) space around a point-source of gravity. For example, it does not apply to a regular star where the Schwarzschild radius would be calculated to be within the interior of the star. So it is doubtful that it could be accurately applied to our observable universe which contains a substantial amount of matter, regardless of whether you consider our matter distribution to be homogeneous or not.

I also think that the Schwarzschild solution takes no account of the Hubble scale expansion of the universe. My guess is that Schwarzschild just isn't applicable to a self-expanding region. Such a region should be expected to behave quite differently from a black hole, for reasons that simply aren't captured in the Schwarzschild equation.

Jon

 

[jal]

All you need to ask yourself are two questions.
“Was all the mass of the universe ever contained is a radius less than R = 2GM/c2 ?”
http://en.wikipedia.org/wiki/Schwarzschild_radius
The Schwarzschild radius
If the mass collapses to a radius less than R = 2GM/c2, where G is the gravitational constant and c is the speed of light, then nothing (including light) can escape from inside this radius. It is called the event horizon or the Schwarzschild radius.
The Schwarzschild radius of an object is proportional to the mass.
------
Second question to ask yourself.
”Was the black hole bigger than 3 solar masses?”
http://en.wikipedia.org/wiki/Primordial_black_hole
One way to detect primordial black holes is by their Hawking radiation. All black holes are believed to emit Hawking radiation at a rate inversely proportional to their mass. Since this emission further decreases their mass, black holes with very small mass would experience runaway evaporation, creating a massive burst of radiation. A regular black hole (of about 3 solar masses) cannot lose all of its mass within the lifetime of the universe (they would take about 10^60 years to do so). However, since primordial black holes are not formed by stellar core collapse, they may be of any size. A black hole with a mass of about 1012 kg would have a lifetime about equal to the age of the universe. If such low-mass black holes were created in sufficient number in the Big Bang, we should be able to observe some of them exploding today.
----------
Conclusion: (if the answer to the above two questions was YES), then we are still in a black hole. Or if you prefer, within the “cosmic horizon”.

 

[Garth]

But as you have been told jal, you are still using an inappropriate expression,

R &lt; \frac{2GM}{c^2},

the Schwarzschild solution, which only applies to a static spherical mass in otherwise empty space.

Unless that is you are proposing that all the mass of the universe was concentrated into a small sphere situated in an infinite and empty space, which is not the understanding of the Big Bang.

In the cosmological solution to Einstein's field equation the appropriate expression is one for density, and the question remains:

"Is \rho &gt; \frac{{3H_0}^2}{8\pi G} or not?"

i.e. "Is the universe closed - finite and unbounded - or not?"

Garth

 

[jal]

Hi Garth!
Since you are advocating a different formula than that of a black hole then I will ask a clarification.
Do you support the claim, that the picture of the Cosmic Background Radiation is a picture of the universe as it was 400,000 years after the big bang?
Do you support, that when applying the energy density formula for a black hole, the result is that we are looking at the interior of a black hole?
Do you agree, that the picture of the Cosmic Background Radiation contains all of the matter of the universe?
You said,
..."the Schwarzschild solution, which only applies to a static spherical mass in otherwise empty space"...
Should not be used
By your statement, How can you justify the concept of black holes within our universe?
Everyone is using the Schwarzschild solution in their papers and everyone "knows" that a black hole is not static and is not in empty space.

You then said,
..."Unless that is you are proposing that all the mass of the universe was concentrated into a small sphere situated in an infinite and empty space, which is not the understanding of the Big Bang."

I beg to differ ... as will others.. and I do not want to divert into a discusion, which has been done too many times, "of what does the universe expand into."

 

[Garth]

You are confusing two different solutions of the same Einstein Field Equation that are applicable to two different situations.

In the first situation all the mass is concentrated in a spherically symmetric mass set in otherwise empty space. This is the One-Body or Schwarzschild Solution.

The expression I quoted from you, R &lt; \frac{2GM}{c^2}, is the condition on the radius of that mass for a BH.

If that condition holds then the mass would concentrate at the singularity at the centre and that radius, the Schwarzschild radius, will be the radius of the Event Horizon that forms around it.

In the second situation all the mass is spread out homogeneously and isotropically throughout the universe. This is the Cosmological Solution.

The other expression I stated, \rho &gt; \frac{{3H_0}^2}{8\pi G}, is the condition for the Critical Density above which the universe is closed in on itself, finite and unbounded. It is sometimes called the Closure Density.

The universe is not, of course completely homogeneous, it has lumps in it, such as you. Some of those lumps of mass may satisfy the first condition in which case they will form a BH.

When I look back to the CMB I do look at all the mass (visible and invisible) on my light cone back to around 400,000 year after BB, however I am not looking into the interior of a BH, I am looking back towards the BB naked 'singularity'.

Do not confuse the two separate solutions to the Einstein Field Equation.

Garth

 

[jal]

The expression I quoted from you, , is the condition on the radius of that mass for a BH.

If that condition holds then the mass would concentrate at the singularity at the centre and that radius, the Schwarzschild radius will be the radius of the Event Horizon that forms around it.

Your statement is not accepted by everyone. There are numerous papers dismissing the singularity.

You are accusing me of being stubborn.

it has lumps in it, such as you.

I shall return the comment by saying that you are closed minded and will not investigate a possibility that you dislike.
When applying the energy density formula for a black hole, the result is that we are looking at a picture of the Cosmic Background Radiation that shows the interior of a black hole?
The only way that you can dismiss this conclusion is by writing a paper that shows that we have somehow exited from that black hole and are now outside of the black hole looking at it from the outside.
Of course you will need to refute the papers by Fulvio Melia.

 

[Garth]

I agree that the concept of a singularity is contentious, however as far as GR is concerned Hawking and Ellis show in The Large Scale Structure of Space-Time that there is no way of escaping a singularity at the centre of a BH, or at the beginning of the present expansion phase of the universe, if certain reasonable conditions are met.

Of course approaching the singularity itself would lead to unreasonable conditions in which it is not unreasonable to hypothesise that GR breaks down.

Nevertheless whether there are true singularities under these extreme conditions, or not, does not alter my argument and the fact that you are consistently confusing two separate solutions to Einstein's Field Equation.

In that sense I am calling you stubborn.

My comment about being a lump was not intentionally rude, the universe is not homogeneous on smaller scales. If it were not you and I would not exists, for whether you like it or not, we are both 'lumps'!

As far as FM is concerned I refer you to #47

Originally Posted by Fulvio Melia View Post

Hi Patti:
...
...
Please note that this does not mean we live inside a black hole.
...

Best wishes,
Fulvio

Garth

 

[jal]

The math says that we are in a black hole. NOT ME! SOOO... DON'T FOLLOW ME FOLLOW THE MATH.

 

[jambaugh]

The math says that we are in a black hole. NOT ME! SOOO... DON'T FOLLOW ME FOLLOW THE MATH.

The math says nothing except what the physical assumptions imply.
Trace your assumptions before you take the math as saying anything.

Here, I'll help... the Schwarzschild solution presumes flat boundary conditions. This is distinct from the cosmological question where there is no boundary per se or the issue of global topology and boundary conditions is the variable in question.

BTW pleas don't "yell" i.e. all caps.

 

[jal]

Hi jambaugh!
My assumptions are that I have been informed correctly and that I'm lacking information.
"... and boundary conditions is the variable in question..."
I'm open for more info.
I'm aware of the the standard inflation model. (That's the one that I've been taught.)
Why is the "black hole model" not being considered?

 

[jal]

Assumed facts that I have learned.
There are 10^80 particles in the universe and they must fit into a sphere with a diameter of 400,000 LY.
Today, the particle sizes are approx. 10^-18m.
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Question
What is the size of the particles at 400,000 years after the big bang so that they can fit into this horizon?
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With my questionable calculations, I get that the particles would have had to be 2.29 times smaller than 10^-18 to fit into the size of the universe at 400,000 years after the big bang.
Therefore, as the universe expanded, from 400,000 LY, the particles would also need to expand and stopped expanding at 10^-18.
In order to get particles at 10^-18 they would have to expand and stop expanding at less than one billion years after the big bang. At that size, the universe would be big enough to contain the 10^80 particles of the standard model.
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Problems
The expansion rate from 400,000 to one billion would be too fast.
Particles are not suppose to be expanding.
Those high energy particles, (smaller than 10^-18), would be creating a cascade of photons and particles, (smaller than 10^-18).
Those high energy particles do not exist in the Standard Model.
There is no mechanism to stop expansion of the particles and have the universe continuing its expansion.
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Possible solutions
Add more particles between the age of 400,000 and a billion. (Merging with more black holes, Reheating.)
Move the CBR from 400,000 to a billion year.
Keep hoping to find those high energy particles that are suppose to exist below 10^-18 ---> Planck scale.
---------
What do your calculations give you?