The Universe is Not a Black Hole

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?

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64 Responses to The Universe is Not a Black Hole

  1. Patrick says:

    “For the universe, there is no such outside region.”

    We don’t know from what the Big Bang sprung or what lies outside the observable universe. We cannot know these things because we have absolutely no information from before the Big Bang or outside the observable universe.

    One can make guesses. One can have interesting ideas. But one can’t know.

    Making such statements of certainty, as quoted above, limits and warps our ability to think accurately about the possibilities.

  2. George Musser says:

    Nicely put. In what ways is a de Sitter horizon similar or dissimilar to a black hole horizon?

  3. Tod R. Lauer says:

    A simple question about attempts to calculate Rs for the Universe. The one talk that I saw where this was done, the speaker omitted DE, which can be viewed as negative matter, from the integral. I’m not sure that even a naive calculation of Rs even makes sense to begin with in a DE-dominated Universe…

  4. Sean says:

    Patrick– true enough, I was implicitly assuming that the universe is described by a Friedmann-Robertson-Walker cosmology. That’s an excellent approximation for the observable universe.

    George– the similarities are sometimes overstated. The BH horizon is a feature of the spacetime, once and for all; the de Sitter horizon is different for each observer.

    Tod– you can do whatever integral you like, since the point is that the universe won’t really collapse to a singularity. There is a singularity in the past, and in the past dark energy was not very important.

  5. ericTAMO says:

    Since it is *currently* impossible to escape our universe it is reasonable to suspect that it is a black hole.

  6. Sean says:

    I should clarify about de Sitter horizons — if the universe is dominated by a permanent vacuum energy (which is plausible), there are “places outside that we can’t reach,” since they are accelerating away from us. This would be true even in a perfectly empty universe, which doesn’t really resemble a black hole. But more importantly, those places are different for every observer; there is not one “interior” region and the rest “exterior,” which is why it’s not very black-hole like.

    Of course if you insist on calling it that, go ahead; it’s a free country.

  7. slw says:

    Hold on, I was under the assumption that the claims made about the universe being a black hole are generally made with regards to the observable universe, not the universe as a whole. That would certainly leave plenty of the rest of the universe to escape to, no? As far as I know, nobody considers the observable universe to be the whole universe.
    Also, is it not true that a photon fired from earth would indeed never be able to escape the observable universe? As it is moving away from earth at c, it would forever remain observable to us, so you can indeed never escape the observable universe, much like a black hole.

    To me it seems the biggest difference between the observable universe and a black hole is that it lacks a singularity, and because of that, it lacks a common event horizon for all observers.

    Also, it is probably just not very useful to think about the observable universe in that way. It is however, fun 😛

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  9. Clifford says:

    “a region of space from which nothing, including light, can escape” sure sounds like our universe. I didn’t think I was in a black hole before, but I sure do now! 🙂

  10. Lord says:

    If there were an outside, we might see matter falling into our universe or gravity from outside having an effect inside. Sounds like a research program to me.

  11. Sam Gralla says:

    Now answer a harder question: what makes a perfectly good physicist go crazy late in life? And–more importantly–how do we make sure it doesn’t happen to us?

  12. Sergiy Koshkin says:

    As I understand, the interior of a Schwarzschild black hole as a spacetime does have Big Bang and Big Crunch, hence both expanding and contracting phases, see http://arxiv.org/PS_cache/arxiv/pdf/0804/0804.3619v2.pdf p.5-6.

    However, the ‘space’ inside is anisotropic with topology of a cylinder. So it definitely looks nothing like our universe. Interestingly enough, it has neither a center, no a singularity. The singularities are in the past and future of any observer (Big Bang and Big Crunch).

    The weirdest thing though is that the ‘outside’ consists of two causally disconnected regions and the black hole serves as a wormhole between them. An observer from one can only see the other after crossing the horizon, with no hope of return.

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  14. KiwiDamien says:

    Hi Sean,

    Working directly from wikipedia’s definition that a black hole is a region from which “nothing can escape” the universe (if there is nothing outside it) is in fact a region from which nothing can escape. It is an example where the precise statement matters, at least if talking with mathematicans (sort of like [0,1) has a supremum and an upper bound, but no maximum value). The statement “nothing can escape” does not imply the existence of somewhere to escape to; the reason that someone could not escape is that there is nowhere to escape to!

    Of course the problem is that wikipedia’s definition is colloquial rather than technical. In order to define a black hole, most books first need to describe asymptotic null future infinity of a geodesically complete spacetime. Provided you can do that defining a black hole is simple — it is the region that does not lie in the causal past of future null infinity. At least this is the definition in Wald’s book. Of course this definition does not satisfy many people as it is chosen to be precise and allow us to prove theorems but suffers from severe drawbacks:
    – It does not work in non-asymptotically simple spacetimes
    – Relies on you identifying physics and hence
    – Is a global definition and not a local one.

    When stated this way, the question of whether or not the universe is a black hole we have two possibilities:
    1) That our universe is asymptotically simple. In this case there is a future null infinity in the completion and some null rays will reach it. Therefore there are points in the universe not contained within a black hole.
    2) We cannot describe future null infinity, and so our definition does not apply to this class of spacetimes.

    You may argue that this is the tail wagging the dog — the definitions should be altered to be useful to science and not the case that we set the definitions in stone and then showhorn science into them. I would agree that trying to generalize the notion of horizon and black hole (as has been done by Hayward and others) is a worthwhile endevor but we should not mix-and-match. We should either go from an argument (such as your nice example of the universe resembling a white hole if anything) about how we think an object should be classified and use it as a guide in our classification system OR start with a definition and see what the consequences are. (Which may later led you to the conclusion that the classification system is poor, and should be redefined, but you would probably start a separate paper or post for that.)

    In this post you have (at least in my opinion) misapplied the colloquial definition from wikipedia as well as argued why the universe should not be classified as a black hole.

    I hope this does not come off as harsh – I think fundamentally we don’t have any disagreement. It is just a personal preference if we start from a definition we apply it strictly, or we collect ideas to try and give us an idea of what a useful definition of a category should include. I see many arguments in religion and politics where people try doing both at once, and usually because they want to redefine something to be what they want, but carry all the emotional baggage the term already carries so they won’t let us know explicitly they are changing the definition.

    Thanks for the postings, and I agree that the white hole example is a useful one.

  15. miller says:

    The radius of the observable universe is actually somewhat larger than the Hubble length. The Hubble length is 13.8 billion light years, but the observable universe has radius 46.5 billion light years. The reason for the difference has to do with the fact that the Hubble distance increases over time at the speed of light. Thus, even if light starts out beyond the Hubble distance, it can eventually catch up to us.

    But it’s only a factor of about three, so in physics-speak, they’re “basically” the same, as Sean said.

  16. chriss says:

    I’m pretty sure I read an essay by Asimov some years ago that made that very claim. I blame him.

    Does anyone else recall that?

  17. Ron says:

    Ned Wright’s FAQ one sentence answer: “The Big Bang is really nothing like a black hole. The Big Bang is a singularity extending through all space at a single instant, while a black hole is a singularity extending through all time at a single point.”

  18. Sean says:

    That’s not really a good answer; the Big Bang and black hole singularities are both spacelike. I.e. the Big Bang extends through all space at a single instant, and the black hole singularity extends through part of space at a single instant.

  19. Lab Lemming says:

    Why is calculating the mass of the universe straightforward? Doesn’t this require observation of galaxies, dark matter estimation, a decent length scale, etc?

  20. Dave says:

    Correct me if I’m wrong, but doesn’t the maximally extended Schwarzschild solution have two completely disconnected regions of spacetime that both have the white hole in their past? So if the FRW solution looks like a white hole, couldn’t this other region constitute an “outside” of our universe?

  21. Sean:

    The gravitational field of a black hole, unlike other characteristics of it contents, extends beyond its horizon, and its effects are ‘easily’ observed.

    Could not very concentrated and ‘large’ masses ‘beyond’ our cosmic horizon be observed by their effects on our side of the horizon – as accelerations away from us – ‘indistinguishable’ from dark energy?

    Wouldn’t that also be ‘required’, if our universe were a black hole?

  22. Charon says:

    Sean: “Note that a spatially flat universe remains spatially flat forever”.
    Not if we can convert enough matter, (1+z)^3, into energy, (1+z)^4! Woohoo!

    Lab Lemming: Sean calculated the density of the universe assuming it was flat (the critical density), which is trivial from setting the curvature to zero in the Friedmann equation. Observations (particularly CMB) tell us that the universe is flat. Some things get easier when you move to larger scales, and you ignore little fluctuations like galaxies 🙂

  23. Bob Zannelli says:

    The Universe is certainly not a black hole. But there does seem to be some connection between global geometry of a given Hubble volume and its entropy content. Inflation enforces the condition of a saturated entropy bound for every Hubble volume of spacetime. Based on this we can understand why the vacuum energy density takes the value it does based on matter density. Of course we don’t know what the mechanism is that gives us Dark Energy. But if gravity is really emergent, a kind of entropic force , as Verlinde has suggested, thinking this way might be helpful. I don’t think this is nonsense but it’s uncertain if it leads anywhere useful.

  24. Frederick von Blabbermaut says:

    Sam Gralla asked: ”
    Now answer a harder question: what makes a perfectly good physicist go crazy late in life? And–more importantly–how do we make sure it doesn’t happen to us?”

    [a] Thinking that one can understand GR without studying it and thinking hard about it for many years.

    [b] A timely retirement, and a vow not to publish anything thereafter.

  25. Frederick von Blabbermaut says:

    Ned Wright allegedly said: “The Big Bang is a singularity extending through all space at a single instant, while a black hole is a singularity extending through all time at a single point.”

    Oh dear. I’m afraid I would flunk a student who made an error that flagrant. And he doesn’t even have the excuse of being a particle theorist.