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I was surprised to only recently notice that

An object of any density can be large enough to fall within its own Schwarzschild radius.

Of course! It turns out that supermassive black holes at galactic centers can have an average density of less than water's. Somehow I always operated under the assumption that black holes of any size had to be superdense objects by everyday standards. Compare the Earth to collapsing into a mere 9mm marble retaining the same mass, in order for the escape velocity at the surface to finally reach that of light. Or Mt. Everest packed into one nanometer.

Reading on about this gravitational radius, it increases proportionally with total mass.

Assuming matter is accumulated at a steady density into a spherical volume, the volume's radius will only "grow" at a cube root of the total volume and be quickly outpaced by its own gravitational radius.

Question: For an object the mass of the observable universe, what would have to be its diameter for it to qualify as a black hole (from an external point of view)?

Would this not imply by definition that:

  • The Earth, Solar system and Milky Way are conceivably inside this black hole?
  • Black holes can be nested/be contained within larger ones?
  • Whether something is a black hole or not is actually a matter of perspective/where the observer is, inside or outside?
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Related: physics.stackexchange.com/q/2268/2451 –  Qmechanic Apr 1 '12 at 10:00
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This might answer your question: blogs.discovermagazine.com/cosmicvariance/2010/04/28/… –  WIMP Apr 5 '12 at 10:01
    
@WIMP That at least is one examination I am finding satisfactory and not relying on circular reasoning (eg. disqualified because already expanding) –  Marcos Apr 5 '12 at 10:21
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Food for thought: if time stops at the event horizon (for an outside observer), for inside, my intuition suggests, time should go backwards. So for matter, that's already inside when the black hole forms, it won't fall towards a singularity but would fall outwards towards a the event horizon due to this time reversal. So inside there would be an outward gravitational force. It would be fascinating if it turns out that all this cosmological redshift, and expansion we observe, is just the effect of an enormous event horizon outside pulling the stuff outwards. –  Calmarius May 5 '13 at 20:44
    
Since the event horizon of a black hole depends on the future it could be that we are inside a black hole. –  jjcale Aug 23 '13 at 19:29

7 Answers 7

up vote 1 down vote accepted

No. The large scale geometry of the universe is described by the Friedmann-Lemaitre-Robertson-Walker metric.

The geometry of the spacetime of a black hole (in its simplest form) is described by the Schwartzschild metric.

These are totally different solutions of the Einstein Field Equations. For example, in the Schwarzschild metric, the spacelike part of the spacetime is curved, in the FLRW metric it is planar.

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I'm inclined to believe this large scale universe may not be simply connected, as described from your first link. –  Marcos May 8 at 16:46
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@Marcos Afaik introducing topology in general relativity is a wellgoing and very interesting area since the 90s, but currently there is no experimental data supporting it. As we see, the large-scale parameters of the universe are the same everywhere, and this is what the Friedman-model uses. Some (currently highly speculative) models are predicting significant changes in the large-scale metric on an extremely long distance. –  Peter Horvath May 8 at 17:03
    
This answer is wrong, the inlating Universe CAN be described by a black hole metric with the region beyond the cosmic horizon taking the role of the BH interior. –  Dilaton May 9 at 7:09
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@Dilaton How? Could you cite a reference? –  Peter Horvath May 9 at 7:20

Hmm... The Schwarzschild radius prevents light from getting out of a black hole, but not from getting in, doesn't it? If so, then what matters is that the Schwarzschild radius is bigger than the observable universe, while the opposite proves nothing, no?

WIMPs link to the discover magazine article is interesting, but I noticed that one of the counterarguments is that the universe is expanding, not contracting. But, if we were inside a black hole, wouldn't expansion be exactly what we'd experience?

Consider this: if we're inside a black hole, then everything is moving towards the singularity. Things closer to the singularity are moving faster, and vice versa. This means that for us, everything else is moving away from us (because things closer to the singularity move faster, and we move faster than things further away from the singularity).

The expansion wouldn't be entirely uniform, and I may be wrong, but I seem to recall reading recent data that in fact implies that it isn't.

I am going to out myself as a big fan of the "living in a black hole" idea. I like how intuitively the "pull" of a singularity would explain everything moving forward in time, or even possibly be an explanation for "dark energy" aka acceleration of the apparent (from our point of view) expansion of the universe (since we are moving closer to the singularity).

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Good point. That being the case, shouldn't it be possible to check which direction(& maybe distance) the singularity is from us, by relative rates of nearing or receding bodies around, assuming a fixed geometry? Else if everything is receding from us at the same rate in every direction, the absurdity of what that implies is intentional. –  Marcos Jan 28 '13 at 10:36
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Yes, it should be possible, and one might argue that we already found signs of it: "Great Attractor" and "dark flow": [en.wikipedia.org/wiki/Great_Attractor] –  user1459524 Jan 28 '13 at 12:54
    
"what that implies": By that I meant it'd imply we are at the center of things / We, as the observer of everything receding from us uniformly, must therefore be at the singularity. (But that's just absurd! ....right?) –  Marcos Nov 26 at 16:25

In a certain sense we are "almost" in a black hole. If we ignore the accelerating expansion for a moment, then it turns out that the energy density of the observable universe is nearly exactly what one would need to form a black hole. This is why the geometry is nearly flat and why there was a debate for many years about whether the universe would collapse or expand forever. This critical energy density is about 10^-29 grams per cubic centimeter, and the real universe is less than a percent over this value. However, the fact that most of this energy density is comprised of some mysterious "dark energy" complicates the simple relation between energy density and whether or not something forms a black hole. Thus, as pointed out above, our universe is not a black hole, it is more like a de Sitter space. de Sitter spaces share an area/entropy relation similar to black holes but are fundamentally different. (The relationship to black holes is tantalizing close, while being different enough to thwart an easy comparison.)

By the way, if the universe were in a black hole, this wouldn't have any immediately drastic consequences. It would, however, mean that we are bound to hit the singularity eventually, which would be what we call the Big Crunch. This, however, seems unlikely based on current cosmological data.

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This is not quite right, although it is a reasonable heuristic. In the cosmological situation you never form a true black hole, because the big-crunch and a black hole are qualitatively different situations. –  Ron Maimon Apr 5 '12 at 3:17

This is not exactly right, because the universe is expanding. You can't treat matter which is outside the cosmological horizon (if the concept is even meaningful, which I don't admit) as part of the matter which is gravitating, because it is not in causal or gravitational communication with matter here. The bounds you give are for matter sitting still.

The proper view is that the universe itself is an inside-out black hole, with a cosmological horizon that surrounds us. In this point of view, the matter inside the universe and the cosmological constant are, together, responsible for the shape of the enclosing horizon, or black hole.

But this is not a black hole, in that it isn't singular in the center, only (in certain energy models) singular in the past.

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The geometry of this is baffling. We're in the middle of this black hole. If space continues on forever, then so does the "interior" of the black hole. The casual disconnection is also baffling to me. Objects within this black hole interacted with us (gravitationally and otherwise) in the past but are no within the event horizon. I suppose this is the case for "ordinary" black holes, but let's not forget - the gravity of an in-fallen object still interacts gravitationally with the rest of the universe after it passes the horizon. –  Alan Rominger Apr 1 '12 at 23:44
    
While I'd have to better formulate my problem with the "because the universe is expanding" argument by itself (similar to the chicken-or-egg justification used on why the Big Bang didn't remain confined to its own possible black hole)‌​, I find causal disconnection more acceptable, given even gravity waves are limited to c, not instant propagation. The inside-out black hole-ness is a novel idea, like the notion we're on an "unbound" 3D surface of a 4-spatial dimension sphere...Know of any research links supporting that? –  Marcos Apr 5 '12 at 14:49
    
Without being a scientist and far to weak to draw any mathematical background to this, I like the idea of being inside a black hole. To me, this puts Big-bang, Universe expansion and Dark matter into other perspective. The Big-bang (and cosmic microwave background) are the matter entering this black hole; Expansion is explained by the fact we are deeper in the hole that the new matter entering it and Dark matter is the matter we cannot see because it is even deeper in the hole ... Well, this my point of view, as far as I can explain it. Hope there's most sophisticated background like this :) –  CitizenInsane Oct 19 '12 at 20:06

No one yet pointed out that the currently established radius of the observable universe actually doesn't meet the Schwarzschild radius requirement to make it a black hole in itself. Not meant to be misleading but this was deliberate in my original post, as it is significantly close in magnitude and doesn't much change the essence of my question.

Here were my assumptions:

Now 10B ly is smaller than 46B ly.

However it's a substantial fraction, and a universe merely 10 times more massive, achieved by a cube-root extension of the 46B ly radius (assuming continued mean density into the additional volume required) to 99 B ly would already fall inside its new corresponding Schwarzschild radius of 100 B ly.

Even considering the non-Euclidean topology of space at these distances, 10x would not be far off from the actual factor required to meet the Schwarzschild criteria for a black hole.

The reason this question still intrigues me as relevant is that intuitively, I'd find it highly unlikely that the actual universe's size matches so closely to the observable universe's. Similar to the coincidence we're at the center of the universe.

One more wrinkle--and I'm almost ready to hear again about needing to keep within distances that are causaly(gravitationally) connected, where borders are defined by receding at light speed. No doubt this is merely a limitation of my understanding, but let's say I in Poland and you in Norway technically have different reaches of causality. Though our spheres largely overlap, our causally-connected/observable universes may not be 100% the same, and this effect is slightly more pronounced if you happen to be on the other end of the Great Wall. To me this further makes a well-defined event horizon at universe scales rather nebulous, suggesting black holes have possibly relative placement?

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This answer: physics.stackexchange.com/a/1904/7743 for the other question says if we squeeze all mass into a black hole it would be 5 times bigger than the observable universe. –  Calmarius May 5 '13 at 21:03

Consider two observers, A and B. A is observing B falling into a black hole. A observes B both slowing down in time, and getting blue shifted as B falls toward the event horizon this continues forever, as B can never be observed to actually pass into the event horizon from A's vantage point. B observes none of this. Instead, what B observes is A accelerating in time, and becoming red shifted, assuming the red shifted light of the universe hitting B does not kill him, B will continue to fall toward the singularity. B may observe itself as it crosses the event horizon, but there will be no indication that B has crossed it. Presumably, when B crosses the event horizon the universe will no longer be visible, as it would be too far red shifted to see, and the radiation so compressed that no discernible data from the exterior universe could be gleamed. At some point in B's observations will continue forever, because as B increases in velocity due to gravity pulling him ever faster toward the singularity time will slow for him, until B reaches the speed of light and event upon which B's observations will "stop" but as it approaches the speed of light (no matter how rapidly), the time it takes to get to that speed will be observed as infinite time to B.

So if our whole universe is falling toward a singularity, we will never observe it to "hit the singularity" and the universe's accelerated expansion, might be due in part to our decelerating perception of time. Which makes way more sense to me, than this mysterious dark energy/matter nonsense.

The universe is expanding, and this could be explained as a gravitational tidal force. Given point A and B where B is closer to the singularity than A, then there would be a difference in the gravitational forces acted on A and B dragging them into the black hole, and their relative distance would appear to "expand" or stretch. It could be that the geometry of the observable universe falling into a black hole could be such that it could be observed that the universe were expanding when it is actually only being stretched due to gravitational tidal forces.

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Only when you're not looking at it. When you are looking, presuming it's expanding, it is a white hole.

Seriously, if we are inside a true singularity, then all of time is included within it, so issues of redshifting, movement, even gravity, etc., are "red herrings" -- artifacts of the observer's frame of reference that misinform oneself. The real issue, then, is what is the real relationship between the observer and the scale of the universe?

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I didn't downvote, but I am having a hard time understanding the meaning/relevance of this answer, and what it contributes about physics. –  Marcos Jan 28 '13 at 12:26
    
Well, do you know about the Copenhagen interpretation of the wave function? –  Mark J Jul 16 at 0:08
    
eg. specifically, the uncertainty principle? that the closer you try to measure something, the more it taints the outcome? What does that have to do with the price of eggs? :) –  Marcos Jul 18 at 9:19
    
Copenhagen interpretation has nothing to do with the uncertainty principle. –  Mark J Jul 20 at 20:22

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