Are we inside a black hole? 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?

 A: 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:


*

*Even by conservative estimates, the observable universe's radius is established at ~46 billion lightyears.

*An object of observable mass of 3 × 10^52 kg. would have to be contained within a Schwarzschild radius of ~10B ly
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?
A: 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.
A: We probably aren't inside a black hole, but the idea isn't unreasonable.
The current accepted answer says

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 Schwarzschild metric. These are totally different solutions of the Einstein Field Equations.

That's technically true, but it misses the point. Of course a black hole in its simplest form is incompatible with FLRW cosmology. It's a vacuum solution that contains no matter anywhere at any time. It's also incompatible with real-world black holes, which form from collapsing matter. That's no reason to conclude that black holes can't exist, and it's no reason to conclude that we aren't inside a black hole.
In fact, the formation of a more realistic black hole by collapsing matter is basically a big crunch. This paper in section 6 has a family of exact solutions for black holes forming by the collapse of spherically symmetric dust. In the special case that the dust is homogeneous, the internal geometry of the dust is FLRW, because that's the only geometry with the necessary symmetries. If you take a solution of this form with the dust initially at rest, and glue it to a time-reversed copy of itself, you get a recollapsing FLRW universe surrounded by vacuum in which the big bang and big crunch singularities are identical with the past and future Schwarzschild singularities. So combining a FLRW universe with a black(+white) hole is not just possible but fairly natural.
A few decades ago, this would have been a plausible enough model for the real world. But current evidence suggests that our universe isn't going to recollapse. If there's no future singularity, then there's no black hole.
As Ron Maimon said, you can think of the ΛCDM universe as "collapsing" outward to an inside-out black hole, but that isn't really the same thing.
A: 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 Schwarzschild 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.
A: 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.
A: A black hole is little more than a spatially closed, gravitationally bound quantity of matter with an escape velocity greater than or equal to the speed of light, but for a black hole to have a validated existence, it must be perceived from OUTSIDE, not inside.  In a universe-sized black hole, it would not seem like a black hole from within.  The mass inside the black hole would equal the mass necessary to render spacetime flat, and if more matter fell in, the radius would increase proportionately, and the ratio would remain constant.
The real issue is whether or not our calculations of the mass of the universe are accurate; it is most certainly not so.  Dark matter, never seen, never measured but only postulated from gravitational expectations that were not met by current models suggest one mass, conventional empirical (measured, not inferred) evidence suggests a much smaller mass.  Which is correct?  If history is a reliable guide, neither one.
It is essentially irrelevant if we are or are not in a black hole.  If we can leave our universe, where would we go?  Currently unanswerable without an external frame of reference, which would be a Catch-22.
Our meager understanding of gravity (we still do not know what it is, only how it behaves locally) is insufficient to answer any of these questions.  Speculating on an answer is indulging in intellectual mythology.  Without better data, we are just making up solutions to a question we do not fully understand, and that is not only bad science, it is lousy thinking.
And for the record, math as a form of symbolic logic is devious - it can be used to support or decry, but unless it is used as a proof, it is only distracting and often misleading.  Formulae are inherently limited, and as such can be rightfully accused of cherry-picking the data to only use terms that support the hypothesis. Math cannot suggest or imply a solution any more than a hammer can recommend house design.  People anthropomorphize math too frequently, when in fact, it is people who suggest, and people who infer.  And frequently, they do so with poor judgement until enough data is available to make the conclusion self-evident.
We have not proven that the universe is expanding.  We have not validated the mass of the known universe.  We have not even accurately measured the distances to the most distant objects yet observed.  All we have done is observed motions on a galactic scale, and applied gravitational formulae that were derived locally with an infantile understanding of gravity itself. Hubble accurately measured red shifts of distant objects, but in his 1942 paper in the Sigma Xi Journal questioned the relation between his observations, actual motion and an expanding universe.  If he had the courage to question the very thing that gave him fame, we should have the courage to honor his skepticism and wait until we have an ANSWER and not a guess born out of impatience and hubris.
A: Although some problems have been raised in Black Hole Cosmology (movement towards the singularity, past singularity and future singularity problem, the expansion of the universe, etc.), these problems are likely to be solved.
1.Black Hole Cosmology
The Black Hole Cosmology is very likely to hold true if the following four things are true,
1)Finite Universe
We do not yet know whether the universe is finite or infinite. However, in my personal opinion, infinity is a mathematical notion, and there seems to be no infinite in physical reality. Even flat space-time does not guarantee an infinite universe (infinite mass-energy distribution). Since the age of the universe is finite and the propagation velocity of the field is also finite, the mass distribution is considered to be finite. Therefore, if we exclude the infinite universe, we face the problems 2)~4).
2)Schwarzschild's radius equation
If we find the size at which the mass distribution with the average mass density of the present universe forms a black hole.
$R = \frac{{2GM}}{{{c^2}}}$
${R_{UB}} = \sqrt {\frac{{3{c^2}}}{{8\pi G\rho }}}  = 14.3Gly$
The above expression means that if the present universe has a critical mass density $ρ_c$ value and the size is approximately $R_{UB}=14.3Gly$ or more, this region becomes a black hole.
3)Observed average density
The order of 5~6 hydrogen atoms per m^3
4)The observable universe 46.5Gly (*the entire universe much larger than the observable universe.)
Currently, we estimate that the size of the observable universe is larger than 14.3 Gly, and the entire universe is estimated to be larger than the observable universe 46.5Gly, so our observable universe inevitably exists inside a huge black hole called the universe.
The Black Hole Cosmology is the inevitable conclusion of the above 4 items.
2) is an equation that has been verified in two different theoretical systems (Newtonian mechanics and general relativity), 3) and 4) is on a very solid foundation, and even if 3) and 4) have some errors, the entire universe is estimated to be much larger than the observable universe. Even if the average density is lower than the current observation, the much larger entire universe inevitably renders the universe a black hole. This is because when the universe becomes R times larger, the density required to become a black hole decreases by $1/R^2$.
2.Weaknesses of the Black Hole Cosmology
1)In a black hole, all matter is compressed into a singularity, so there is no space for humans to live. There is no almost flat space-time that could contain the observable universe inside a black hole.
2)In the black hole, singularity exist in the future, and in the universe, singularity exist in the past. Black hole and the universe are opposites.
3)The universe is expanding. Inside a black hole, all matter must contract at a singularity. The two models show opposite phenomena. It is difficult to explain the expansion of the universe inside a black hole.
Although this objection(or Weaknesses) appears to be clear and well-grounded, in fact, this objection also has its own weaknesses.
1)The proposed weakness does not break the argument 2)~4) of the Black Hole Cosmology. Whatever the weakness , if 1) ~ 4) does not collapse, the Black Hole Cosmology is very likely to hold.
2)Most physicists and astronomers believe that the singularity problem will be solved either using quantum mechanics or in some unknown way, so there will be no singularity.
In other words, in the process of solving the singularity problem, there is a possibility that the singularity problem of the Black Hole Cosmology will also be solved.
3)Since the singularity exists in the Schwarzschild solution, the Schwarzschild solution must be changed for the singularity problem to disappear. That is, among the elements constituting the Black Hole Cosmology, the "2)Schwarzschild radius equation" is affected.
For the singularity to disappear, there must be a repulsive force inside the black hole. Due to this repulsive force, an uncompressed region inevitably exists inside the black hole.
The remaining problem is, "Could an uncompressed region be larger than the observable universe?"
[Solutions to the problems of Black Hole Cosmology]
Weakness 1)In a black hole, all matter is compressed into a singularity, so there is no space for humans to live. There is no almost flat space-time that could contain the observable universe inside a black hole
Solution
1.The singularity problem is known as a flaw in general relativity, and considering the gravitational action of the gravitational field, there is a possibility that the singularity problem can be solved
The fundamental principle of general relativity states that "all energy is a source of gravity". However, the field equation created by Einstein did not fully realize this principle.
The energy of the gravitational field must also function as a gravitational source. Einstein was also aware of this, and for over two years, beginning in 1913, he worked to formulate a field equation that included the energy-momentum of the gravitational field. However, because it was difficult to define the energy of the gravitational field in general relativity, Einstein could not complete the field equation including the gravitational action of the gravitational field. So, the singularity problem and the dark energy problem came into existence.
2.Gravitational self-energy or Gravitational potential energy
For uniform, spherical distribution,
${U_{gs}} =  - \frac{3}{5}\frac{{G{M^2}}}{R}$
In the generality of cases, the value of gravitational self-energy is small enough to be negligible, compared to mass energy $Mc^2$. So generally, there was no need to consider gravitational self-energy. However the smaller R becomes, the higher the absolute value of $U_{gs}$. For this reason, we can see that $U_{gs}$ is likely to offset the mass energy in a certain radius.
Thus, looking for the size in which (negative) gravitational self-energy becomes equal to (positive) mass energy by comparing both,
$|{U_{gs}}| = | - \frac{3}{5}\frac{{G{M^2}}}{{{R_{gs}}}}| = M{c^2}$
${R_{gs}} = \frac{3}{5}\frac{{GM}}{{{c^2}}}$
This equation means that if mass $M$ is uniformly distributed within the radius $R_{gs}$, gravitational self-energy for such an object equals mass energy in size. So, in case of such an object, (positive) mass energy and (negative) gravitational self-energy can be completely offset while total energy is zero. Since total energy of such an object is 0, gravity exercised on another object outside is also 0.
Comparing $R_{gs}$ with $R_S$, the radius of Schwarzschild black hole,
${R_{gs}} = \frac{3}{5}\frac{{GM}}{{{c^2}}} = \frac{3}{{10}}{R_S}$
This means that there exists the point where negative gravitational self-energy becomes equal to positive mass energy within the radius of black hole, and that, supposing a uniform distribution, the value exists at the point $0.3R_S$, about 30% level of the black hole radius.
In case of the smallest stellar black hole with three times the solar mass, ${R_S} = 9km$. $R_{gs}$ of this black hole is as far as $3km$. In other words, even in a stellar black hole with smallest size that is made by the contraction of a star, the mass distribution can't be reduced to at least radius 3km.
3.Black hole does not have a singularity, but it has a Zero Energy Zone
From the equation above, even if some particle comes into the radius of black hole, it is not a fact that it contracts itself infinitely to the point $r=0$. From the point $R_{gs}$ (or $R_{gs - vir}$), gravity is 0, and when it enters into the area of $R_{gs}$ (or $R_{gs - vir}$), total energy within $R_{gs}$ (or $R_{gs - vir}$) region corresponds to negative values enabling anti-gravity to exist. This $R_{gs}$ (or $R_{gs - vir}$) region comes to exert repulsive gravity effects on the particles outside of it, therefore it interrupting the formation of singularity at the near the area $r=0$.

Fig.1. Internal structure of the black hole. a)Existing model b)New model. If, over time, the black hole stabilizes,the black hole does not have a singularity in the center, but it has a zero (total) energy zone.
4.Inside a sufficiently large black hole, there is enough space for intelligent life to exist
A black hole has no singularity, has a Zero Energy Zone with a total energy of zero, and this region is very large, reaching 15% ~ 30% of the radius of the black hole. Inside a sufficiently large black hole, there is an area where intelligent life can live.

For example, if the masses are distributed approximately 46.5Gly with the average density of the current universe, the size of the black hole created by this mass distribution will be 491.6Gly, and the size of the Zero Energy Zone will be approximately 73.7Gly ~147.5Gly. In other words, there is no strong tidal force and a region with almost flat space-time that can form a stable galaxy structure is much larger than the observable range of 46.5 Gly. The entire universe is estimated to be much larger than the observable universe, so it may not be at all unusual for us to observe only the Zero Energy Zone (nearly flat space-time).
Weakness 2)In the black hole, singularity exist in the future, and in the universe, singularity exist in the past. Black hole and the universe are opposites
Solution
Just because a singularity exists in the future in a black hole and a singularity in the universe in the past does not negate the Black Hole Cosmology.
In order to solve the singularity problem of black hole, there must be a situation in which repulsion outweighs attraction (gravity) below a certain size. In a situation in which repulsion outweighs attraction, the area must expand. If this expansion is converged into the past, a singularity appears, and thus the singularity direction becomes a form that exists in the past.
In a stellar black hole, an object enters the black hole from the event horizon, and in the case of the universe, it is only a case of expanding from a singularity toward the event horizon. It is still a phenomenon that occurs inside a universe black hole.
When an object is thrown upwards in Earth's gravitational field, it looks different when it rises up and when it comes down from its apex, but both events are just two aspects of a single event in the same gravitational field.
Weakness 3)The problem of cosmic expansion inside a black hole. The universe is expanding. It is difficult to explain the distance between galaxies inside a black hole
Solution
There are several ways to explain the expansion of the universe inside a black hole (formed when only mass energy is considered without considering gravitational self-energy).
Consider the initial state of the universe. The entire universe is larger than the present observable universe, $46.5Gly$. Since we do not know the size of the entire universe, after thinking about the state in which all the mass-energy in the present observable universe is concentrated in a very small area, let's apply this logic to the entire universe.
As calculated above, the size of the ZEZ produced by all mass-energy in the observable universe is approximately $73.7Gly$ ~ $147.5Gly$, and the size of the universe black hole is $491.6Gly$. Since these materials are concentrated in a very small area, the negative gravitational potential energy of this area exceeds the positive mass energy and corresponds to a negative mass state as a whole. The negative gravitational potential energy acts as a repulsive force on the positive masses, so it expands.
This expansion is accelerated up to at least ZEZ ($73.7Gly$ ~ $147.5Gly$), and since it is in an accelerated state, expansion continues beyond ZEZ. As time passes, when the distribution of mass is outside the ZEZ, the mass state within the ZEZ is a state in which the positive mass energy is greater than the negative gravitational potential energy, so the total mass (within the ZEZ) is a positive mass, and the attraction is applied to the masses outside the ZEZ. This will have the effect of slowing the expansion.
The universe expansion at the time of the big bang is because all matter inside the cosmic black hole started in a region smaller than the ZEZ, and there is a possibility that it corresponds to the accelerated expansion process up to the ZEZ. The size of the ZEZ created by the mass distribution of the observable universe is $73.7Gly$ ~ $147.5Gly$, but the present observable universe is passing $46.5Gly$.
When considering the expansion in the early high-density state of the universe, there is a problem that people mistakenly think that this event is the escape of matter from the inside of the black hole created by the total mass of the universe to the outside to form galaxies or stars.
The black hole event horizon created by the total mass of the universe is very large compared to the area where the total mass of the universe is gathered. In this case, the black hole refers to a black hole formed by considering only mass-energy without considering gravitational potential energy. In other words, in the Black Hole Cosmology model, matter does not escape the universe black hole, but has not yet reached the event horizon of the universe black hole (formed when only mass energy is considered without considering gravitational potential energy).
Refer to my paper: Problems and Solutions of Black Hole Cosmology
A: 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.
A: 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).
A: They marked it "duplicate" but I think it adds:
As I suppose we all accept, the universe started as an unintuitive singularity—either, "Let there be light," or "The Big Bang". Something from nothing expanded and at luminal speeds (or greater).
I read about this "Planck Epoch": the time from zero to approximately 10−43 seconds. When there was no such thing as mass and gravity, a bunch of energy was being massaged for this eventuality but nothing could hold it together. It is still expanding to this day.
My question is simply this:
Could the upper limit of energy that the Black Hole can contain be dependent on how close this energy is before it reaches the levels of the Planck Epoch?
After it consumed enough matter (energy), the conditions for gravity to work would no longer exist, just like during the Planck epoch. Extreme amount of energy... unbounded now.
The whole universe is the result of a supermassive Black Hole that swallowed enough to produce Planck epoch energies thus disabling gravity (and all fundamental forces).
Simple... like Einstein liked it!
A: The entropy of a black hole is maximized. This is not the case for the matter that makes up the Earth; the entropy is not zero, but it's not maximized either. Thus, we do not live in a black hole.
A: 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?  Since, there's no Grand Unified Theory,  that little factor "G" at the beginning of Newton's formula is pretty fungible (i.e. a lot of degrees of freedom to stipulate what mass is, for example).
