People sometimes ask, “Is the universe a black hole?” Or worse, they claim: “The universe is a black hole!” No, it’s not, and it’s worth getting this one straight.
If there’s any quantitative reasoning behind the question (or claim), it comes from comparing the amount of matter within the observable universe to the radius of the observable universe, and noticing that it looks a lot like the relationship between the mass of a black hole and its Schwarzschild radius. That is: if you imagine taking all the stuff in the universe and putting it into one place, it would make a black hole the size of the universe. Slightly more formally, it looks like the the universe satisfies the hoop conjecture, so shouldn’t it form a black hole?
But a black hole is not “a place where a lot of mass has been squeezed inside its own Schwarzschild radius.” It is, as Wikipedia is happy to tell you, “a region of space from which nothing, including light, can escape.” The implication being that there is a region outside the black hole from which things could at least imagine escaping to. For the universe, there is no such outside region. So at a pretty trivial level, the universe is not a black hole.
You might say that this is picking nits, and the existence of an outside region is beside the point if the inside of our universe resembles a black hole. That’s fine, except: it doesn’t. You may have noticed that the universe is actually expanding, rather than contracting as you might expect the interior of a black hole to be. That’s because, if anything, our universe bears a passing resemblance to a white hole. Our universe (according to conventional general relativity) has a singularity in the past, out of which everything emerged, not a singularity in the future into which everything is crashing. We call that singularity the Big Bang, but it’s very similar to what we would expect from a white hole, which is just a time-reversed version of a black hole.
That insight, plus four dollars or so, will get you a grande latte at Starbucks. The spacetime solution to Einstein’s equation that describes a universe expanding from the Big Bang is very similar to the time-reversal of a black hole, but you don’t really learn much from making that statement, especially because there is no outside; everything you wanted to know was already there in the original cosmological language. Our universe is not going to collapse to a future singularity, even though the mass is enough to allow that to happen, simply because it’s expanding; the singularity you’re anticipating already happened.
Still, some folks will stubbornly insist, there has to be something deep and interesting about the fact that the radius of the observable universe is comparable to the Schwarzschild radius of an equally-sized black hole. And there is! It means the universe is spatially flat.
You can figure this out by looking at the Friedmann equation, which relates the Hubble parameter to the energy density and the spatial curvature of the universe. The radius of our observable universe is basically the Hubble length, which is the speed of light divided by the Hubble parameter. It’s a straightforward exercise to calculate the amount of mass inside a sphere whose radius is the Hubble length (M = 4π c3H-3/3), and then calculate the corresponding Schwarzschild radius (R = 2GM/c2). You will find that the radius equals the Hubble length, if the universe is spatially flat. Voila!
Note that a spatially flat universe remains spatially flat forever, so this isn’t telling us anything about the universe now; it always has been true, and will remain always true. It’s a nice fact, but it doesn’t reveal anything about the universe that we didn’t already know by thinking about cosmology. Who wants to live inside a black hole, anyway?
>> So the universe as a whole is spatially flat, but small parts of it are not?
The universe is flat in an average* sense.
* note that the notion of average is very poorly defined in this context.
your reasoning is backwards. there is no “outside”, therefore nothing can escape, therefore the universe IS a black hole. the fact the behavior doesn’t conform to what you “might expect the interior of a black hole to be” means your expectations are wrong, nothing else.
>>your reasoning is backwards. there is no “outside”,
Reasoning is not the issue – the Universe is *mathematically* not like a black hole (in general) – only some universe have a future finite conformal horizon which means there are parts of the existing universe which we can never visit.
@ 51: Thanks. I know, I was specifically asking about this “on average” statement. How does one determine in physics whether something is “on average” homogenous? Particularly when subsets of that space appear to be exceedingly non-homogenous?
There does not seem to be a straightforward way in either physics (or biology) to talk about irregularities found in nature. Computer scientists are little better off because they can start off from a binary string right off the bat, based on rigid definitions of machines and their input and output. But in the real world, nobody has defined these things. Real systems work differently – the universe computes itself, so to speak. The machine and the tape are one. What I am trying to say is that before you make entropy calculations..etc, one has to determine how to achieve a universal method of description of the physics of a particular segment of space. Currently, their seems to be no such method. Kolmogorov complexity and related studies do no attempt to approach this problem. Like I said, they *assume* a solution to this problem, and start off from there, which is meaningless.
Can someone please correct my logic. If “there was a singularity in our past” then we must still be within its event horizon. The Big Bang didn’t blast our proto-bits out beyond the Schwarzschild radius-that would be impossible, right? All the Big Bang could do was create new space but still within the horizon. If we are not on the inside of a BH how did the universe escape that primordial singularity?
It was a different kind of singularity to the one you see at the centre of the schwarzschild black hole. The black hole is a singular point in space, the universe was singular everywhere (and if it is infinite, still everywhere infinitely so).
just restating what pat said:
if the big bang density was infinite, that sounds like a black hole to me.
since you cant escape from it, we are still in that black hole.
>> if the big bang density was infinite, that sounds like a black hole to me.
since you cant escape from it, we are still in that black hole.
While it sounds like the same thing to you, it isn’t – mathematically, they are different.
Sean says, “it’s very similar to what we would expect from a white hole, which is just a time-reversed version of a black hole.” But that implies the stuff was inside a BH safely behind the horizon and then flew out beyond the horizon-the reverse of falling into the BH. Also it implies that there was a singularity and then the density was too small to cause a collapse, which would look like stuff flying out of the singularity to form a star. But these sound like impossible events and so the trick is in the phrase “very similar” and that is what I don’t understand.
I confess that I have found very little written about this conundrum and would greatly appreciate a pointer. My question is best stated as, “what rules govern the state of the universe just after the Big Bang?” Was there great enough density to cause a BH collapse or not? I understand that the Big Bang singularity was in all space at once, not a single point in a greater space but how do you get around the density question? Was space expanding too fast to allow a collapse? If so then there is an interpretation of the collapse formula that I don’t understand.
First, let me make it clear that I have no credentials and no idea what I’m talking about. But that’s no excuse for not having an opinion, is it?
Seems to me that all of the arguments for “not a black hole” presume that we know what our measurements are actually telling us. But what do those measurements look like from an observer outside of the universe? Could it be that the dark energy is actually collapsing and if you look from this outside perspective, that our measurable universe ia actually static and not expanding? That somehow the measurements we make are merely seeing the differential between dark energy and the rest of it, and we assume that ours is the correct perspective, but in fact everything we assume is flawed because our Flat World tools simply cannot measure in enough dimensions for us to determine what is happening.
>> But what do those measurements look like from an observer outside of the universe?
Within GR – the thing that we use to describe and explain the universe – there is no outside
Well, I have two things to say about all this: To think this all happened circumstantially is absurd. God is great; and the heavens prove so!
If one allows black holes to be nested then there could be exterior and interior regions to a black hole universe. In fact, if our universe were a black hole, then there would indeed be nesting of black holes, since our universe certainly contains black holes.
This possibility of nested black holes provides a mechanism for the multiverse – among all the multitude of nested black holes, some would have conditions which are not propitious to producing stars, galaxies and life, whereas some might, including our own.
The Bekenstein equation is
S_bek= 2*pi*R*E/(hbar*c)
Therefore
2*pi*R*E/(hbar*c) = pi*R^2*c^3/(hbar*G)
since
R=c/H
E= c^5/(2*G*H)
V= 4*pi*c^3/(3*H^3)
rho_bek= E/V = 3*H^2*c^2/(8*pi*G) = Rho_Hubble when k=0
This gives us
S_Hubb= pi*c^5/(hbar*G*H^2)
And there you have it.