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How large would a black hole need to be to overcome inflation and pull all matter one day into a big crunch?


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Been having some wild speculative thoughts, but I want to cross examine them with guidance on this question. Depending on the answer, my thoughts may or may not be valid. If there is some kind of known and verified limit on this then my speculation means nothing. 

So how large can a black hole potentially get? 

What I'm imagining is a Colossus of a black hole, with a strong enough gravitational pull that all matter everywhere is destined to fall into it. 

Can such a thing exist?

Correction: Overcome Expansion? May have messed up the terminology a bit.

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According to current theory, didn't the entire Universe spring from a minute "Black Hole" smaller than a proton. Then expanded outwards. To create trillions of stars, galaxies and so on.

Given the wide vista of prospects allowed by such a theory,  would you rule anything at all out,  as physically impossible?

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6 minutes ago, Charles 3781 said:

According to current theory, didn't the entire Universe spring from a minute "Black Hole" smaller than a proton. Then expanded outwards. To create trillions of stars, galaxies and so on.

According to many people, the whole universe was born from nothing.

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Just now, Kartazion said:

According to many people, the whole universe was born from nothing.

Don't you mean, "according to scientists", the whole Universe was born from nothing?    

Suppose you were asked, "Where did your  computer come from?"  And you said:  "That's a meaningless question - it came from nothing."   How would you respond?

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4 minutes ago, Charles 3781 said:

Don't you mean, "according to scientists", the whole Universe was born from nothing?    

Suppose you were asked, "Where did your  computer come from?"  And you said:  "That's a meaningless question - it came from nothing."   How would you respond?

Scientists have alerted to this fact. Suddenly this gives people wise like us.

But yes I know. Let's say the universe at its beginning was no bigger than a pinhead.

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31 minutes ago, Charles 3781 said:

According to current theory, didn't the entire Universe spring from a minute "Black Hole" smaller than a proton.

No. It was a singularity such as those predicted at the center of BHs, but was not from a BH itself. 

32 minutes ago, Charles 3781 said:

Given the wide vista of prospects allowed by such a theory,  would you rule anything at all out,  as physically impossible?

Yes. For example, I’m pretty sure it didn’t come from Santa Claus. 

58 minutes ago, MSC said:

So how large can a black hole potentially get? 

Approximately 50 Billion times the size of our sun. 

https://www.newscientist.com/article/dn28647-black-holes-have-a-size-limit-of-50-billion-suns/

59 minutes ago, MSC said:

Can such a thing exist?

No, not according to our current mathematical models. 

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Black holes are very small in relation to their mass. 

The whole Milky Way is somewhere between 100-200 thousand light years across. Yet its Schwarzschild radius is about 0.31 light years only.

On the contrary, the accelerated expansion is only noticeable beyond the range of billions of light years. So black holes would never overcome expansion. The mass would have to be ridiculously big.

You can do the comparison yourself.

 

G=6.674×10−11N⋅m2/kg2

c=3×108 ms-1

1 light year = 3×108 ms-1 × 365×24×3600 s

M = (1 billion light years)× c2 /2×G

Somewhere around 6 × 1042 kg I think. 1030 Milky Ways... Ridiculous

A million million million million million Milky Ways.

No way.

Edited by joigus
Corrected data diameter Milky Way
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As Joigus says, the gravity produced by a BH is no different than from any other equivalent mass.
If expansion can overcome the gravity of galaxy clusters, it can similarly overcome the gravity of a BH composed of the masses of the equivalent number of stars in that galaxy cluster.

There is no upper limit on BH size.
There is only a limit to how much you can feed them.
Once they 'eat' all close by mass via their accretion disc, they can't overcome farther out stable orbiting material, and stop growing.
Direct collapse, however,without going through star lifetimes, is a totally different mechanism.

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1 hour ago, joigus said:

Black holes are very small in relation to their mass. 

The whole Milky Way is somewhere between 100-200 thousand light years across. Yet its Schwarzschild radius is about 0.31 light years only.

On the contrary, the accelerated expansion is only noticeable beyond the range of billions of light years. So black holes would never overcome expansion. The mass would have to be ridiculously big.

You can do the comparison yourself.

 

G=6.674×10−11N⋅m2/kg2

c=3×108 ms-1

1 light year = 3×108 ms-1 × 365×24×3600 s

M = (1 billion light years)× c2 /2×G

Somewhere around 6 × 1042 kg I think. 1030 Milky Ways... Ridiculous

A million million million million million Milky Ways.

No way.

 

56 minutes ago, MigL said:

As Joigus says, the gravity produced by a BH is no different than from any other equivalent mass.
If expansion can overcome the gravity of galaxy clusters, it can similarly overcome the gravity of a BH composed of the masses of the equivalent number of stars in that galaxy cluster.

There is no upper limit on BH size.
There is only a limit to how much you can feed them.
Once they 'eat' all close by mass via their accretion disc, they can't overcome farther out stable orbiting material, and stop growing.
Direct collapse, however,without going through star lifetimes, is a totally different mechanism.

A ridiculously big amount of mass and matter. 10^30...

Know ye of such a large amount of matter, presently unaccounted for in observations save for gravitational and lensing effects on other matter?

What would the scale of the accretion disk of such a monster be like?

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27 minutes ago, zapatos said:

This Youtube video does a pretty good job of explaining what I could have been more clear on. You might like this.

 

Really enjoyed this! Thank you for sharing.

Isn't the scale of mass and Schwarzschild radius relative though? Let say you put me into an indestructible space craft and shrink me down to the size of a microbe and throw me into the accretion disk of a black hole. How would I perceive my orbit around that black hole and is it a terminal velocity that will one day see me gobbled up? What if I'm orbiting some other massive object in the same orbit of the black hole as me?

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And I though Zap and his YouTube friend had done a good job of explaining.

OK, one more time...
The Earth is orbiting the Sun at a radial distance of 150 million km.
We now start compressing the Sun. When it is half its current size, the Earth still feels the same gravitational attraction and remains in orbit at 150 Mkm. When it is one tenth of its current size, the Earth still orbits at 150 Mkm, and feels the same gravity. When it is 1/1000 of its current size, the Sun still has the same mass, and the Earth is still orbiting at the same radius of 150 Mkm, so it still feels the same gravity.
However, when the Sun is compressed past its Schwarzschild radius,    2GMsun/c^2 , or about 6 km across, it is enclosed by an event horizon, which means that, for the mass of the sun, a 3 km radial separation requires an escape velocity faster than the speed of light.

https://en.wikipedia.org/wiki/Schwarzschild_radius

IOW, the event horizon goes black because no light can reach us any longer. Yet the Earth is still happily orbiting at 150 Mkm, and feeling the same gravity.

So, to recap, if our Sun was a Black Hole, at the current distance from the sun we would feel exactly the same gravity as we currently do.
If we were to move closer to the Sun, since as a Black Hole it is vastly smaller, we would feel an increase in gravity, until we get to about 3 km radial separation, at which point no force in the universe could keep us from falling into the event horizon ( its gravity would be THAT strong ).

 

Yes, mass is directly proportional to Schwarzschild radius, but I'm not sure I follow or understand the rest of your questions.
Please re-phrase or clarify.

Edited by MigL
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1 hour ago, MigL said:

However, when the Sun is compressed past its Schwarzschild radius,    2GMsun/c^2 , or about 6 km across, it is enclosed by an event horizon, which means that, for the mass of the sun, a 3 km radial separation requires an escape velocity faster than the speed of light.

 

1 hour ago, MigL said:

Yes, mass is directly proportional to Schwarzschild radius, but I'm not sure I follow or understand the rest of your questions.
Please re-phrase or clarify.

So the only way in this scenario for the earth to fall into our sun, turned BH, is if the earth is within 3 km radial separation of the event horizon or for the mass of the BH to increase so that the required radial separation to stop escape velocity also increases? Or is it always 3km no matter how much the mass of the BH increases? 

Maybe the more appropriate way to ask my original questions; how would the universe look differently to how it does now, if the mass attributed to dark matter was to be found in unknown collosal black holes found in voids in the cosmic web? Would our galaxy have even formed? 

In the wikipedia you sent me in the other thread, it said the image on the right was what a galaxy spiral might look without taking into account the effects of dark matter and the one on the right was taking into account the effects of dark matter. What would it look like if the gravitational effects of dark matter were attributable to galaxy external collosal black holes? All around. 

If my questions are still unclear I can only apologise. When I can find the time I'll track down the key readings that all kind of led me to this hypothesis, but this isn't my formal area of expertise at all. I'll probably have to learn a lot more to either ask what I need to ask or figure out for myself if my hypothesis is impossible.

Thank you for your patience, I'm learning a lot from you and others here but there are probably explanatory gaps that are hard to overcome without my having more experience and knowledge of physics and mathematics.

Edit: By the way I don't buy or jump to complete faith in any hypothesis I think of, I'm not afraid to look foolish if I ask what appears to be a dumb or ignorant question. I've even got questions about a counter hypothesis that Dark Matter is Anti-Matter but I think the good thing about trying to be creative is that you can learn a lot about how things actually are when the hypothesis is shot down.

Edited by MSC
Disclaimer of self-fallibility acknowledgement.
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The thread's question needs interpretation, and I might be interpreting it differently than others. I think that what you're asking is how much mass you would need to make everything in the universe gravitationally bound to it, despite the current rate of expansion.

If I'm thinking about it right, any constant rate of expansion will result in a constant-size cosmic horizon, beyond which it is impossible for matter to be gravitationally bound across that distance. The reason is that the matter would have to be falling in faster than the speed of light, to overcome the expansion of space between it and the mass. The horizon is determined by expansion alone, so making a more massive BH won't help... except...

If you had matter right on the cosmic horizon, you'd need to basically have it falling in at a speed of c to overcome expansion. That would imply a BH with an event horizon at the same radius as the cosmic horizon??? (assuming Schwarzschild BH) But then, if you had a BH even close to that size, matter on the cosmic horizon would be a lot closer to it than if it were a point mass, so wouldn't it fall in anyway? Or does it work out that the gravitational influence of a BH is still the same as if it were a point mass?

This seems really weird, because even if we completely ignore expansion for a moment, wouldn't this mean that the gravitational influence of a BH is roughly proportional to 1/r^2, while the mass is proportional to 1/r, no matter how big it is? That seems to imply that if you could have a BH of unlimited mass, you could make it so that the Schwarzschild radius is so large that an object outside it is so extremely far away from the center of the BH that the gravitational acceleration is small, even if it is near the horizon. Am I thinking about this correctly? How would an infalling observer describe the BH? It seems that the event horizon (a lightlike surface) would still pass by it at the speed of light, despite minimal acceleration. Meanwhile it seems like another observer, hovering farther away, outside the horizon, could easily avoid falling in, and see that same event horizon as stationary. Where's the error in my thinking?

 

Back to expansion, would it even make sense to talk about a constant rate of expansion of spacetime, in a volume that is entirely occupied by a massive BH? The BH curves the spacetime so extremely that the volume inside the horizon is not a part of the same spacetime outside??? Does curved spacetime expand the same as flat spacetime? Would a volume containing a large BH expand the same as a volume of empty space?

Edited by md65536
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11 hours ago, MSC said:

Know ye of such a large amount of matter, presently unaccounted for in observations save for gravitational anSd lensing effects on other matter?

Not enough in the visible universe. You would have to go beyond the cosmic horizon (3-odd billion light years away) and pick up a lot that was lost when the universe was inflating more than a 3-odd billion years ago. And that's impossible.

We suspect lots and lots of matter to have been lost forever beyond the cosmic horizon.

Other users are suggesting different ways of understanding your question, though. That's interesting.

Black holes are usually associated with very intense gravitational fields, but that's because they are behind their horizons; they are extremely compressed. But as pointed out by MigL, the outer field at a distance far enough away is indistinguishable from the field of any other source of the same mass.

Be aware though, that the farther away you go, the more intense is the effect of energy vacuum, and the feebler is the "source effect" one. So you would never be able to compensate by accreting local mass. I hope the argument is clear.

They pull, not only in different directions, but with opposite varying tendencies depending on the distance.

I think that's key to  say; no, it would not be possible.

Still IOW, you're trying to compensate for k'r with a -k/r2 by playing with k. There will always be a distance r such that your "compensation" breaks down.

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10 hours ago, md65536 said:

The thread's question needs interpretation, and I might be interpreting it differently than others. I think that what you're asking is how much mass you would need to make everything in the universe gravitationally bound to it, despite the current rate of expansion.

If I'm thinking about it right, any constant rate of expansion will result in a constant-size cosmic horizon, beyond which it is impossible for matter to be gravitationally bound across that distance. The reason is that the matter would have to be falling in faster than the speed of light, to overcome the expansion of space between it and the mass. The horizon is determined by expansion alone, so making a more massive BH won't help... except...

If you had matter right on the cosmic horizon, you'd need to basically have it falling in at a speed of c to overcome expansion. That would imply a BH with an event horizon at the same radius as the cosmic horizon??? (assuming Schwarzschild BH) But then, if you had a BH even close to that size, matter on the cosmic horizon would be a lot closer to it than if it were a point mass, so wouldn't it fall in anyway? Or does it work out that the gravitational influence of a BH is still the same as if it were a point mass?

This seems really weird, because even if we completely ignore expansion for a moment, wouldn't this mean that the gravitational influence of a BH is roughly proportional to 1/r^2, while the mass is proportional to 1/r, no matter how big it is? That seems to imply that if you could have a BH of unlimited mass, you could make it so that the Schwarzschild radius is so large that an object outside it is so extremely far away from the center of the BH that the gravitational acceleration is small, even if it is near the horizon. Am I thinking about this correctly? How would an infalling observer describe the BH? It seems that the event horizon (a lightlike surface) would still pass by it at the speed of light, despite minimal acceleration. Meanwhile it seems like another observer, hovering farther away, outside the horizon, could easily avoid falling in, and see that same event horizon as stationary. Where's the error in my thinking?

 

Back to expansion, would it even make sense to talk about a constant rate of expansion of spacetime, in a volume that is entirely occupied by a massive BH? The BH curves the spacetime so extremely that the volume inside the horizon is not a part of the same spacetime outside??? Does curved spacetime expand the same as flat spacetime? Would a volume containing a large BH expand the same as a volume of empty space?

This is quite a charitable interpretation of my question and I'd like to thank you for altering some of the parameters of it so that it actually made sense. 

I'm glad people are aware that I am only dealing in complete hypotheticals for the sake of testing how my imagination is trying to explain to me how gravity, expansion, BHs and Dark matter all fit together in the same universe. Since I don't know how to use Math to do it. 

Rolled up in my question when I read back on your reply, is a thought. Why are things expanding more rapidly than most models can account for? What is missing from the models to explain this? The only thing that makes any sense to me is unknown sources of gravity that we aren't seeing. The only explanation my mathematically uneducated brain can conceive of is that Dark matter is responsible. So how could dark matter have a gravitational force powerful enough to explain the rate of expansion and why the rate of expansion is sometimes described as not uniform based on variance in expansion rates when we look at the behaviour of different galaxies? 

We often hear people say that Dark Matter doesn't interact with regular matter, does that mean it doesn't interact with itself either or can dark matter clump together the way regular matter can? If so, why couldn't it also form black holes? 

Thank you for everyone's patience with my questions. I'm doing my best to try to keep up and I apologise in advance for any ignorant questions I may ask.

 

 

4 hours ago, joigus said:

Not enough in the visible universe. You would have to go beyond the cosmic horizon (3-odd billion light years away) and pick up a lot that was lost when the universe was inflating more than a 3-odd billion years ago. And that's impossible.

We suspect lots and lots of matter to have been lost forever beyond the cosmic horizon.

Other users are suggesting different ways of understanding your question, though. That's interesting.

Black holes are usually associated with very intense gravitational fields, but that's because they are behind their horizons; they are extremely compressed. But as pointed out by MigL, the outer field at a distance far enough away is indistinguishable from the field of any other source of the same mass.

Be aware though, that the farther away you go, the more intense is the effect of energy vacuum, and the feebler is the "source effect" one. So you would never be able to compensate by accreting local mass. I hope the argument is clear.

They pull, not only in different directions, but with opposite varying tendencies depending on the distance.

I think that's key to  say; no, it would not be possible.

Still IOW, you're trying to compensate for k'r with a -k/r2 by playing with k. There will always be a distance r such that your "compensation" breaks down.

I'm doing what now? I'll have to take your word that the math of what I'm doing is explainable that way. Thank you for your patience.

I'm unfamiliar with the term "Energy Vacuum." Looking up now! Thank you for the guidance. :)

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19 minutes ago, MSC said:

This is quite a charitable interpretation of my question and I'd like to thank you for altering some of the parameters of it so that it actually made sense. 

I'm glad people are aware that I am only dealing in complete hypotheticals for the sake of testing how my imagination is trying to explain to me how gravity, expansion, BHs and Dark matter all fit together in the same universe. Since I don't know how to use Math to do it. 

Rolled up in my question when I read back on your reply, is a thought. Why are things expanding more rapidly than most models can account for? What is missing from the models to explain this? The only thing that makes any sense to me is unknown sources of gravity that we aren't seeing. The only explanation my mathematically uneducated brain can conceive of is that Dark matter is responsible. So how could dark matter have a gravitational force powerful enough to explain the rate of expansion and why the rate of expansion is sometimes described as not uniform based on variance in expansion rates when we look at the behaviour of different galaxies? 

We often hear people say that Dark Matter doesn't interact with regular matter, does that mean it doesn't interact with itself either or can dark matter clump together the way regular matter can? If so, why couldn't it also form black holes? 

Thank you for everyone's patience with my questions. I'm doing my best to try to keep up and I apologise in advance for any ignorant questions I may ask.

 

 

I'm doing what now? I'll have to take your word that the math of what I'm doing is explainable that way. Thank you for your patience.

I'm unfamiliar with the term "Energy Vacuum." Looking up now! Thank you for the guidance. :)

Sorry, I meant "vacuum energy". It is a part of Einstein's general theory of relativity. It is a term responsible for expansion. The farther away galaxies are from each other, the faster the recede from each other. So the "repulsion" (it's not really a repusive force, it's rather space itself expanding) is proportional to the distance. It also depends on time, increasing exponentially with it, so you would never be able to compensate for it by gathering mass locally. Expansion of the universe will always win eventually, no matter how much mass you cluster together to compensate for it.

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9 hours ago, MSC said:

We often hear people say that Dark Matter doesn't interact with regular matter, does that mean it doesn't interact with itself either or can dark matter clump together the way regular matter can? If so, why couldn't it also form black holes? 

There are two long range forces, gravitational and electromagnetic, and two very short range forces, color and weak ( flavor ).
As far as we know, Dark Matter interacts with all other matter, including itself, gravitationally, but does not interact via the Electromagnetic force at all ( or only extremely weakly ). That means we cannot detect it by electromagnetic means ( no visible, radio, infrared, uv, x-ray or even gamma emissions ), but its gravitational interactions with matter and itself, will produce 'falls' or orbits around its center of gravity. It could also be captured by BH event horizons when it intercepts them.
Dark Matter particles may get very close to each other, or even collide, but, since they don't interact via the color force, they will not clump together like quarks in nucleons, or protons and neutrons n the nucleus due to residual. And since they don't interact electromagnetically, they won't clump like electrons and protons in atoms. So I see very little chance of being able to localize a large enough mass of Dark Matter that it would be able to collapse to a BH.

One type of neutrino is being investigated as a candidate for Dark Matter, so there is the possibility that it also interacts via the weak ( flavor ) interaction, but again, this interaction does not produce bound states.

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19 hours ago, MSC said:

We often hear people say that Dark Matter doesn't interact with regular matter, does that mean it doesn't interact with itself either or can dark matter clump together the way regular matter can? If so, why couldn't it also form black holes? 

Bound systems require a decrease in energy. (If the KE exceeds the magnitude of the PE, the object in question can escape and is therefore not bound.) Normal matter clumps together because their interactions can easily dissipate energy and form bound systems. Gravitational interactions are really bad at dissipating energy. (Gravitational radiation is weak) That’s why DM tends not to clump, or would not (by itself) tend to form a black hole 

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On 10/13/2020 at 4:58 AM, swansont said:

Normal matter clumps together because their interactions can easily dissipate energy and form bound systems.

Why do you refer to something that is so amazing and intricate as ... "clumping"?  I think it's rather amazing that there are positively charged nuclei at all.  You have the strong force overcoming the coulomb force.  There have to be some neutrons in their for larger nuclei, or the nucleus will undergo fission.   The fact that the positive nucleus  is an integer of 1.6x10^-19 coulombs while electrons have a charge - 1.6x10^-19 coulombs, (equal and opposite charge) in spite of their existence at different stages of the big bang seems amazing.    Then, you have the periodic table of 120 elements (I think).  If it wasn't for the weak force, there might be more elements.  All of the atoms that make up the Periodic table engage in "chemistry" which is nothing short of amazing!  You start getting molecules in such large quantities, and they interact together based on Coulomb charges.  I wouldn't expect to get "clumping" until we get up to the electrostatic charges on materials that are a great deal larger. 

I dunno, maybe you meant "clumping" in a more affectionate way.

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4 hours ago, POVphysics said:

Why do you refer to something that is so amazing and intricate as ... "clumping"?  I think it's rather amazing that there are positively charged nuclei at all.  You have the strong force overcoming the coulomb force.  There have to be some neutrons in their for larger nuclei, or the nucleus will undergo fission.   The fact that the positive nucleus  is an integer of 1.6x10^-19 coulombs while electrons have a charge - 1.6x10^-19 coulombs, (equal and opposite charge) in spite of their existence at different stages of the big bang seems amazing.    Then, you have the periodic table of 120 elements (I think).  If it wasn't for the weak force, there might be more elements.  All of the atoms that make up the Periodic table engage in "chemistry" which is nothing short of amazing!  You start getting molecules in such large quantities, and they interact together based on Coulomb charges.  I wouldn't expect to get "clumping" until we get up to the electrostatic charges on materials that are a great deal larger. 

I dunno, maybe you meant "clumping" in a more affectionate way.

1. I didn’t use the term first; I used the same terminology as was used in the question I answered

2. I don’t think there’s any suggestion that this isn’t amazing

3. This is semantics and “clumps together” is perfectly cromulent. Perhaps you have a suggestion of a better word?

4. Is there any objection to the veracity of the science being discussed?

 

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4 minutes ago, swansont said:

1. I didn’t use the term first; I used the same terminology as was used in the question I answered

2. I don’t think there’s any suggestion that this isn’t amazing

3. This is semantics and “clumps together” is perfectly cromulent. Perhaps you have a suggestion of a better word?

4. Is there any objection to the veracity of the science being discussed?

Forgive me.  I didn't mean to sound confrontational.  To me, the building blocks of matter are more like an exquisite puzzle.  Actually, now that I think about the question you were answering, "clump" is a good description to use.  I have never heard of dark matter behaving like anything other than a fluid that is non interactive with charges or photons.  If I were to hazard a guess at what dark matter might be, my answer would be that, probably before the leptogenesis and baryogenesis epochs of the big bang, there might have been a massive energy dump into extremely small non interacting particles, similar to neutrinos, but a lot smaller. 

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While a large local mass-energy density will result in a Black Hole of any size, this will only result in locally large space-time curvature.

A collapse of the whole universe requires a global curvature.
If the mass-energy density of the whole universe ( not just observable ) exceeds a certain amount, then the global curvature will be positive, and the universe will close in on itself and be unbounded but finite ( 3D analogy would be a sphere ), even as it continues its expansion.
If the mass-energy density is equal or less than the critical amount, it will either be unbounded flat, or unbounded hyperbolic ( negative curvature, saddle shape ), and both are destined to expand forever.

The only possibility which supports a re-collapse would be the positive curvature, hypersphere topology universe, but our current observations seem to suggest a global curvature that is very nearly flat, and accelerating expansion.

Edited by MigL
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