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

[Garth]

SMBH's form from the material from this universe that coalesced under its mutual gravitational field in the first place.

The radiation from those SMBHs also comes from the material falling into them, from the accretion disk before the event horizon is reached.

Radiation does not come 'out of' a SMBH, beyond the except for an infinitesimal amount of Hawking Radiation.

We don't know what lies at the centre, singularity or not, and we may never know because of the event horizon.

The Big Bang singularity would be different, if it is a singularity, because it is naked.

Garth

 

[jal]

The radiation from those SMBHs also comes from the material falling into them, from the accretion disk before the event horizon is reached.

I agree, that is what is being claimed.
Let's back up a little bit.
I did some calculations, in a previous post, and I could not get 10^80 particles into the 400,000 lyr sphere.
As a result, I question that there was enough material available to creat that radiation from those SMBHs.
I'm going to assume that my calculations are wrong and that you did your calculations and that the 10^80 particles can fit into the 400,000 lyr sphere.
Let's go over your calculations ... then we can move on and discuss on a common footing.
jal

 

[Garth]

Where did you get 10⁸⁰ particles from?

That is the approximate number of particles in the whole observable universe, not the number that would form a SMBH.

Garth

 

[jal]

I’m not coming up with anything new. I’m just using the information that I have learned.
Speed of light = 300,000 km/sec
Sec, min, hr, day, yr, =60*60*24*365= 525,600
300,000*525,600 = 1.58 *10 ^9 km, = 1.58 * 10^12 cm. = 1.58 * 10^27 protons (proton = 10^-15)
400,000 *(1.58 *10^27) = 6.31 *10^32 proton diameter of CBR

sphere = ( π •d³)/6 = 3.14*(6.31 *10^32)^3/6 = 3.14*(2.51*10^34)/6 = 1.314 *10^34 protons
Densest sphere packing (hex.) will only fill 74.08% of space.
Therefore, 0.7408(1.314 *10^34) = 9.73*10^33 protons in a sphere of 400,000 light years. OR there are aprox. 10^34 protons in the CBR.
Therefore, if there are 10^80 protons in the universe, there is a shortage of 10^46 protons in the universe.
Since the CBR does not reveal a hex. packing pattern, then RANDOM packing is the most likely scenario and random pack only makes up about 64 percent. As a result there would be even less protons in the CBR.
ONLY, if the SMBH came from outside of the THEN size of the universe can we end up with enough particles to make up the 10^80 estimated number of particles in the universe.
NEXT,
Possibly half of all the radiation produced after the Big Bang may be attributed to the SMBH, whose number is now known to exceed 300 million.
Who can do the calculation of how many particles are locked up in those SMBH that cannot contribute to that half of all the radiation produced after the Big Bang?
Don’t forget, if I made a calculating error, then the 10^34 protons in the CBR will not be the right starting point.

 

[Garth]

Your maths and physics are wrong!

What do you intend by calculating the number of protons in the CMB? The CMB is a warm bath of photons.

I’m not coming up with anything new. I’m just using the information that I have learned.
Speed of light = 300,000 km/sec
Sec, min, hr, day, yr, =60*60*24*365= 525,600

Actually 60*60*24*365 = 3.1536x10⁷

300,000*525,600 = 1.58 *10 ^9 km, = 1.58 * 10^12 cm.

You seem to be calculating (incorrectly) the number of kilometres in 300,000 light years. Actually 300,000 light years is = 9.4608x10¹²kms = 9.4608x10¹⁷cms.

1.58 * 10^27 protons (proton = 10^-15)

this is in metres not cms.

400,000 *(1.58 *10^27) = 6.31 *10^32 proton diameter of CBR

Wherre does the 400,000 come from?

I won't go any further, your argument is Not Even Wrong and it is Christmas Eve, I have better things to do!

Garth

P.S. If you want to find out how crowded the protons were at the Last Scattering Surface of the CMB there is an easier way.

The CMB has been red shifted by ~ 1100 since it was emitted at the LSS. This means that linear distances between representative galaxies were 1100 times smaller then.

The volume of the universe was therefore ~10⁹ smaller than now.

The present baryon density is ~ 10^-30 gm/cc which means it was ~ 10^-21 gm/cc at the LSS.

This is far more rarefied than in the best laboratory vacuum, not what you would call crowded!

 

[jal]

jal
Don’t forget, if I made a calculating error, then the 10^34 protons in the CBR will not be the right starting point.

Garth
Your maths and physics are wrong!

The point has been well made and illustrated.
I was being the "straight man". Probably will get interpreted as "an idiot".
I have already pointed out that I get my units and zeros mixed up.
I like your ps. and will include it in my blog
------------
Of course, my calculations are wrong and need to be “fined tuned” to include the electrons because we see the CBR with The hydrogen line.
http://en.wikipedia.org/wiki/Atom
The electron is at 9.11×10-31 kg
Protons at 1.67×10-27 kg
The electron cloud
The smallest atom is helium with a radius of 31 pm, (10^-12) while the largest known is caesium at 298 pm. Although hydrogen has a lower atomic number than helium, the calculated radius of the hydrogen atom is about 70% larger.
Spectra of excited states can be used to analyze the atomic composition of distant stars. Specific light wavelengths that are contained in the observed light from stars can be separated out and related to the quantized transitions in free gas atoms.
The first atoms (complete with bound electrons) were theoretically created 380,000 years after the big bang; an epoch called recombination, when the expanding universe cooled enough to allow electrons to become attached to nuclei. Since then, atomic nuclei have been combined in stars through the process of nuclear fusion to generate atoms up to iron.

A typical star weighs about 2x10^33 Grams, which is about 1x10^57 atoms of hydrogen per star... That is a 1 followed by 57 zeros.
A typical galaxy has about 400 billion stars so that means each galaxy has 1x10^57 X 400,000,000,000 = 5x10^68 hydrogen atoms in a galaxy
There are possibly 80 billion galaxies in the Universe, so that means that there are about: 5x10^68 X 80,000,000,000 = 4x10^79 hydrogen atoms in the Universe.
http://en.wikipedia.org/wiki/21_centimeter_radiation
The hydrogen line
http://en.wikipedia.org/wiki/Timeline_of_the_Big_Bang#Recombination:_380.2C000_years
-------
Merry Xmas

 

[Garth]

Yep, about 10⁸⁰ in the observable universe is the 'ball park' figure.

Garth

 

[hurk4]

A beating heart in a static Schwarzschild shell.

I voted for yes without giving my arguments, which after all I will give here.
1) I am convinced of a bounce preceding the expansion phase. (I think this is according Bojowald; Ashtekar).
2) Now aday’s, I.M.O. it is well accepted that the bounce domain, LQC at t=0, or even the BB in string theory, was not a point but indeed a domain containing high density.
3) If 1) is true, then there was no beginning in time ,(our observable universe did not start; t=0 is the phaseshift moment where contraction changed into expansion).
4) To me it seems not an absolute necessary condition that the maximum density, though very high, at the bounce should become as high as the Planck density.
5) I.M.O. “the cosmological principle” is a kind of boundary condition/specification (obvious very practical to use in most cosmological calculations) but certainly not a physical law. It is, to a certain degree, useful in many macroscopic considerations about our observable universe, but there are deviations and it is certainly not proven by experiments to be valid at even larger scales. Theoretically it seems me to be too big a constraint for further thinking, because it implies that the expansion of the universe is valid at all scales as an extrapolation of the experienced expansion of our observable universe.
6) I.M.O. it is very well thinkable that the cosmological principle is not exact valid at all macroscopic scales. In a kind of absolute sense from our observation site approximately yes, but in a relativistic sense no.
7) If 6) is true then it is imaginable that our verse (bounce) is not unique in space time i.o.w. it might be a concentration domain of energy (mass, black energy, dark energy and the like). See alo my thread “is our bounce unique?”
8) If 7) is true then it is very well imaginable that though the related verse is not static as a whole, its dynamic part can serve as the kernel of a BH/WH with a relative static Schwarzschild horizon. Around this kernel the density is then decreasing and very low, much lower then the density of our observable universe. We can calculate for each average density a Schwarzschild radius provided that this radius is larger then the radius of the domain in consideration and provided that a correction can be made for the influence of the surrounding environment..
I would conclude by saying I voted for yes because, with all my arguments together, I see possibilities for a universe which was never created and which will ever exist where I don’t need to accept a nonsensical nothing, a strange inflation concept or a religious argument which still puts ourselves in a central position. Some of my thoughts I saw already expressed in some posts of this thread but I felt a drive for myself to give you my own picture.
In my view I see our verse as “a beating heart within a Schwarzschild shell; this one beeing one of many in an infinite universe”

 

[marcus]

I voted for yes without giving my arguments, which after all I will give here.
1) I am convinced of a bounce preceding the expansion phase. (I think this is according Bojowald; Ashtekar).
2) Now aday’s, I.M.O. it is well accepted that the bounce domain, LQC at t=0, or even the BB in string theory, was not a point but indeed a domain containing high density.
3) If 1) is true, then there was no beginning in time ,(our observable universe did not start; t=0 is the phaseshift moment where contraction changed into expansion).
4) To me it seems not an absolute necessary condition that the maximum density, though very high, at the bounce should become as high as the Planck density.
5) I.M.O. “the cosmological principle” is a kind of boundary condition/specification (obvious very practical to use in most cosmological calculations) but certainly not a physical law. It is, to a certain degree, useful in many macroscopic considerations about our observable universe, but there are deviations and it is certainly not proven by experiments to be valid at even larger scales. Theoretically it seems me to be too big a constraint for further thinking, because it implies that the expansion of the universe is valid at all scales as an extrapolation of the experienced expansion of our observable universe.
6) I.M.O. it is very well thinkable that the cosmological principle is not exact valid at all macroscopic scales. In a kind of absolute sense from our observation site approximately yes, but in a relativistic sense no.
7) If 6) is true then it is imaginable that our verse (bounce) is not unique in space time i.o.w. it might be a concentration domain of energy (mass, black energy, dark energy and the like). See alo my thread “is our bounce unique?”
8) If 7) is true then it is very well imaginable that though the related verse is not static as a whole, its dynamic part can serve as the kernel of a BH/WH with a relative static Schwarzschild horizon. Around this kernel the density is then decreasing and very low, much lower then the density of our observable universe. We can calculate for each average density a Schwarzschild radius provided that this radius is larger then the radius of the domain in consideration and provided that a correction can be made for the influence of the surrounding environment..
I would conclude by saying I voted for yes because, with all my arguments together, I see possibilities for a universe which was never created and which will ever exist where I don’t need to accept a nonsensical nothing, a strange inflation concept or a religious argument which still puts ourselves in a central position. Some of my thoughts I saw already expressed in some posts of this thread but I felt a drive for myself to give you my own picture.
In my view I see our verse as “a beating heart within a Schwarzschild shell; this one beeing one of many in an infinite universe”

Hurk, i like your argument! I don't see anything to disagree with (except you did not read the question of the poll carefully enough.)

Based on your argument our region of spacetime is OUT THE BACK DOOR of a black hole, so our own Hubble sphere or cosmological event horizon is NOT THE BLACK HOLE HORIZON---which is what the poll asked.

No! According to your picture, the black hole event horizon is BEFORE THE BIG BANG.

So speaking carefully, answering exactly what I asked in the poll (I phrased it carefully for this reason!) you should, by rights, have answered NO.

After the big bang space was expanding too rapidly to form a black hole and the usual horizons that people talk about (cosmological horizon and Hubble sphere) are obviously not the horizon of any black hole. Someone out there could easily exit right across them without any effort. I'm sure you understand this.

I like your picture---which is similar to Smolin's reproductive cosmology picture where black holes also lead to new expanding regions of spacetime. So I will think of you as actually answering no to the poll question as posed.

Does anyone else who originally said "Yes" want to change their opinion to "No"?

 

[jal]

Thanks Garth for accompanying me in this quest for information.
The big bang model has been refined for over 50 years.
Amateurs and students have probably been asking the same questions for 50 years.
All adjustments and refinements came about as a result of these kinds of questions and as a result of new observations from astronomers.
As I understand, now, the only adjustment that needs to be done, to coincide with observations, is those 300,000 million quasars, (black holes), which were formed in the early universe.
To try to answer this problem, Fulvio Melia is doing something different. He is proposing changing the age of the universe to accommodate the necessary time needed for the formation of those black holes. He is proposing two ages:
1) A particle distribution age, 13.7 Gyrs, which we can observe and
2) A Gravity age, which we cannot observe, occupying a sphere of 16.9 billion light years which would be the actual age of the universe.
Our lack of understanding of gravity at small scales, (smaller than a hair), and our inability of “seeing” if gravity is constant on all scales is the main obstacle to moving further in our understanding of the universe.
The cosmic background radiation which has been set at 400,000 years does not contain a baryon density which would indicate a black hole.
However, when doing a “look back” in an expanding universe, the baryon density would have been sufficient to have been in a Schwarzschild radius prior to 400,000 years.
Anything prior to 400,000 years (the CBR) is void of observation.
This is, therefore, another indication of our lack of understanding of gravity.
Did “mother nature” find a way out of the Schwarzschild radius?
Did “mother nature” find a way to avoid Schwarzschild radius?
OR
Is the Schwarzschild radius still there?
From our observations, we cannot detect or interpret any signs of what we understand to be a Schwarzschild radius, (a gravitational cosmic horizon).
As a result, hurk4’s description, “A beating heart in a static Schwarzschild shell” cannot be ruled out.
As an amateur I have many different questions.
Since gravity was also within the 400,000 CBR sphere and since gravity is expanding at the speed of light then as the gravity sphere gets bigger as a result, the space that the particles can occupy gets bigger.
That would imply that the expansion of the universe is due to gravity having an expanding Schwarzschild Radius.
If there was an input of 300 million Super Massive Black Holes (SMBH) after the big bang and before z = 10 then the universe would get an additional expansion phase.
Hummmm! Maybe different sizes of black holes have different properties and behave differently?
What was the Schwarzschild radius before the input of those 300,000 black holes?
Hummmm!
Maybe it was a black hole. Maybe the high energy prior to the 400,000 year was bouncing around for a long time over many cycles of bounce prior to getting an additional input of matter which would increase the Schwarzschild radius past the 400,000 light year.
With the discovery of dark energy as being the main constituent of the universe, new concepts are being considered. (Even that gravity is not a force but a geometric condition.)
Of course, with “accurate number crunching” some of these questions can be eliminated as highly improbable due to our present observations. I hope that Garth and other good “number crunchers” will stick around and help to answer some of these questions.
---------
http://arxiv.org/abs/0712.3545
The Higgs Phenomenon in Quantum Gravity
Authors: R. Percacci
(Submitted on 20 Dec 2007)

http://arxiv.org/abs/0712.4143
Cosmological Plebanski theory
Authors: Karim Noui, Alenjandro Perez, Kevin Vandersloot
(Submitted on 26 Dec 2007)

 

[hurk4]

Hurk, i like your argument! I don't see anything to disagree with (except you did not read the question of the poll carefully enough.)

Based on your argument our region of spacetime is OUT THE BACK DOOR of a black hole, so our own Hubble sphere or cosmological event horizon is NOT THE BLACK HOLE HORIZON---which is what the poll asked.

No! According to your picture, the black hole event horizon is BEFORE THE BIG BANG.

So speaking carefully, answering exactly what I asked in the poll (I phrased it carefully for this reason!) you should, by rights, have answered NO.

After the big bang space was expanding too rapidly to form a black hole and the usual horizons that people talk about (cosmological horizon and Hubble sphere) are obviously not the horizon of any black hole. Someone out there could easily exit right across them without any effort. I'm sure you understand this.

I like your picture---which is similar to Smolin's reproductive cosmology picture where black holes also lead to new expanding regions of spacetime. So I will think of you as actually answering no to the poll question as posed.

Does anyone else who originally said "Yes" want to change their opinion to "No"?

Hi Marcus, you are very nice.

6 times YES. Indeed I did not read the full question and restricted myself to "Are we in a Scharzschild hole?". A shame and my excuses for that!

And indeed No would have been the correct answer to a question like "Does something non existing exist?". Am I wrong if I see kind of a tautology here? In that case such an answer makes no sense. But again I might have misread your question?.

I am curious whether other people voted for yes instead of no!

kind regards
Hurk4

 

[jal]

I’m not ready to quit without getting a few more answers.
1) We still have not taken the effect of the mass of the neutrinos.

Garth
The CMB has been red shifted by ~ 1100 since it was emitted at the LSS. This means that linear distances between representative galaxies were 1100 times smaller then.

The volume of the universe was therefore ~109 smaller than now.

The present baryon density is ~ 10-30 gm/cc which means it was ~ 10-21 gm/cc at the LSS.

This is far more rarefied than in the best laboratory vacuum, not what you would call crowded!

Would we do the same procedure for neutrinos? Is there room for all of them in a 400,000 light year sphere.
http://arxiv.org/abs/astro-ph/0607101
Neutrino masses and cosmic radiation density: Combined analysis
Steen Hannestad and Georg G. Raffelt
06 July 2006
---------
2) We cannot leave without including some kind of number for dark energy.
http://www.physics.ucla.edu/hep/dm04/talks/yunwang.pdf
Model Model-Independent Reconstruction of Dark Energy Density
from Current Observational Data
Yun Wang
UCLA Symposium on Dark Matter & Dark Energy,
Feb 19, 2004
----------
Being an amateur, I can only wait for the answers to the “number crunching” to see if we are within a Gravitational Cosmic Horizon.

 

[marcus]

Thanks Hurk4,
I must sheepishly admit that the shortened headline for this thread was not the full poll question. The question on the poll had an extra condition which one could easily overlook. I hope the comments clarified this for most people.

Specal thanks to several knowledgeable commenters---Garth, Wallace, Pervect, George Jones and others---who carefully explained issues in this thread.

With Hurk's vote changed, the results are 9 Yes out of 47.

It may be that some others want to change their vote, if they are still around and learned something from the thread discussion.
The 9 who voted Yes are:
Amp1, BigFairy, daveb, jal, lightbeing, on30francisco, PaulR, PRyckman, thepassenger48

If any of you find you have second thoughts after following the discussion, please let us know.

 

[Fra]

I voted no opinon because the question seems complex and I'm not sure the standard foundations are satisfactory to even formulate that question yet, or my own understanding is not complete enough to relate to the question.

But I think there are interesting parallells to black holes and systems considered to be "observers". The normal definition of a black hole is made relative to current models.

If we consider a black hole to be an observer, than what is a black hole? Classicaly it seems to be an observer that manages to consume new information without limiting constraint of capacity since the consumed information is added to the systems own capacity. Normally to maintain constant capacity, new information must be matched by emission of information. But it seems a black hole is so dominant that it can control and change it's environment rather than the other way around, that the observer adapts to the environment. I find this parallell fascinating, and it indeed seems to be a desirable skill - I think we all want to grow up to be black holes :) If you can learn how to control the unknown to such an extent that you can adapt any new information without making a choice on what to release.

What are valid "observers": particles? molecules? cells? organisms? solar systems? universes? What's the principal difference except the obvious: complexity?

But then when the quantum behaviour is added it gets worse. If even a black holes leaks, then it seems to suggest that it really doesn't irreversibly consume it's environment.

/Fredrik

 

[PaulR]

Vote Change

I understand from the discussion that:
The density of space would correspond to a 13.7 billion year black hole to an outside observer, but...
A black hole cannot be expanding, so our visible universe fails this second criteria.
Thus we are not in a black hole.

This leads to a few questions:

Is it just a coincidence that the density condition is met?

Does any expansion velocity disqualify or does the expansion have to be above a specific amount?

Best current guess is expansion is speeding up. If it slowed or stopped would the universe then be a black hole if it met the density?

 

[jonmtkisco]

Hi PaulR

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

I don't think that any amount of expansion is consistent with being a black hole. As I mentioned in an earlier post, the Schwartschild solution simply isn't designed to factor in expansion, because black holes are not thought to expand.

If the universe stops expanding and collapses into a singularity, then it will come to resemble a black hole, except that as far as we know there is nothing "outside" of it, which is an obvious difference from a normal black hole.

Jon

 

[marcus]

Jon thanks for spotting Paul's question and responding.
I agree with you.

PaulR, I got distracted with other stuff, sorry not to have gotten back earlier. I see you changed your vote so now we have 8 people who say we are in a Schwarzschild BH with some well-known horizon like the cosmological event horizon or the Hubble radius serving as black hole horizon.
Those 8 people are

Amp1, BigFairy, daveb, jal, lightbeing, on30francisco, PRyckman, thepassenger48

As I said in an earlier post, if anyone has formed a different opinion and wants to change votes that's fine, just post. I will try to catch it more promptly than last time with PaulR

 

[PaulR]

Thank you for these clarifications.
However it leads to more questions:

I don't believe it is accurate to say there is nothing outside of a 13.7 billion light year radius. That radius is only based on the time the universe has existed and the speed of light. There is no reason to believe there is "nothing" beyond that as space expansion almost guarantees there is. Thus observers could exist outside a 13.7 billion light year sphere.

I was also curious, not about the collapse of the universe, but about the condition that would occur if the universe stopped expanding, before it started collapsing. For that however brief moment would the outside observer experience this as a black hole? It would have the exact density and would not be expanding.

Last point - Could you recommend any website that would explain how "the Schwartzschild solution for a black hole is mathematically equivalent to the equation for determining the event horizon of an observable universe." I didn't realize that determining the value of 13.7 billion light years had any relation to the equation for a black hole. I just assumed it was based on observation, while the black hole density calculation was based on theory.

 

[PaulR]

It's been 9 days since I posted.
Is this thread closed?

 

[marcus]

...
I don't believe it is accurate to say there is nothing outside of a 13.7 billion light year radius. That radius is only based on the time the universe has existed and the speed of light. There is no reason to believe there is "nothing" beyond that as space expansion almost guarantees there is. Thus observers could exist outside a 13.7 billion light year sphere.
...

I never heard it suggested that the Hubble sphere, with radius c/H
was any kind of physical boundary. (except in amateur speculation)
in any standard cosmology picture the universe extends right past there without significant change.

to an observer out there 13.7 billion LY from here, things would look pretty much the same as they do here----same density of matter, same kind of galaxies, same nearly flat space.

the most distant stuff we have observed so far is now about 45.6 billion LY from us, this distance is almost the same as the 46-47 billion LY defining the "particle horizon", the most distant matter we COULD currently be observing, given ideal instruments.

I'm not sure the point of what you said, whether it contained a question, but it is indeed a commonly accepted view!
====================

the next thing I don't understand, all observers are in the universe. there is no outside observer.
if the universe stopped expanding and prepared to collapse then we would ALL be, in effect, in a black hole which would NOT have 13.7 billion LY as any kind of horizon. the WHOLE KABOODLE would be destined to collapse, all observers would realize this----that they were all inside what was going to collapse.

It would not correspond to a SCHWARZSCHILD black hole. That is something with a technical meaning. The outside is permanently static from time minus infinity to time plus infinity. For eternity. So it would be incorrect to call it a Schwarzschild BH. But it would definitely be a universe on the way to a big crunch.
And this would involve a much much bigger chunk of space than our little private Hubble sphere with its radius of 13.7.

I think that's about right Paul. Someone can correct me if I've made some error. But I haven't thought much about Crunch because I don't think its in the cards.
There seems to be a consensus nowadays that the universe is on track to keep expanding indefinitely.

 

[Jorrie]

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

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

Jorrie

 

[jonmtkisco]

Hi Jorrie,

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

Jon

 

[Jorrie]

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

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

From Melia's summary:

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

Jorrie

 

[jonmtkisco]

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

Jon

 

[PaulR]

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

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

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

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

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

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

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

 

[Jorrie]

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

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

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

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

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

 

[marcus]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

anyway thanks for the interesting questions!

 

[Haelfix]

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

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

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

 

[marcus]

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

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

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

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

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

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

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

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

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

 

[Haelfix]

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

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

 

[marcus]

...

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

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

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

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

 

[jonmtkisco]

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

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

My calculation is as follows:

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

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

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

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

Jon

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

 

[marcus]

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

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

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

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

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

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

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

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

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

I totally agree with your conclusion!

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

 

[jonmtkisco]

Hi Marcus,

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

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

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

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

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

Jon

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

 

[PaulR]

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

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

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

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

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

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

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

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