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Maybe the big bang did produce a black hole, and we're living inside it? Back in my undergrad physics days, I postulated that our "universe" could be a big bla

Maybe the big bang did produce a black hole, and we're living inside it? Back in my undergrad physics days, I postulated that our "universe" could be a big black hole inside some "extraverse". I worked through classical gravitational calculations to determine, from an estimate of the mass density of the universe, what the Schwarzschild radius (aka event horizon radius) of that black hole would be, and it came out to between 5 and 40 billion light years or so (the density of the universe is hotly debated, see other discussion in this thread about dark matter), which is at least the right order of magnitude.

jobigoud 8y ago
How is it the right order of magnitude? Did you compute that based on the size of the observable Universe? But that's arbitrary, the Universe is way bigger than that.
- Simon_says 8y ago
  No. The input into the equation is the density of matter in space, nothing having to do with the size of the observable universe. On large scales in the visible universe, matter is fairly evenly distributed at a density of about 1 atom of hydrogen per cubic meter. For any constant nonzero density form of matter, if you pack enough of it together in a sphere in a flat spacetime, its Schwarzchild radius will eventually exceed its radius. This is because the Schwarzchild radius is proportional to the mass, but the radius of the actual matter is proportional to the cube-root of the mass. It's a fun thought experiment, but not physically meaningful in this universe because our spacetime is expanding, and the original calculations assume there's nothing at the edge pulling 'outward', but in our universe there is.
  - pdonis 8y ago
    > For any constant nonzero density form of matter, if you pack enough of it together in a sphere in a flat spacetime, its Schwarzchild radius will eventually exceed its radius. You can't do this in flat spacetime, because the matter curves spacetime, and the denser you pack it, the more it curves spacetime.
    - Simon_says 8y ago
      Obviously. The point of the thought experiment was that you start with a universe with no other matter in it that's not expanding, both of which conditions our universe violates.
  - dantillberg 8y ago
    Thank you, you're adding more concrete verbiage to my suspicions that my calculations were too naive: I was only doing classical, pre-General-Relativity, calculations. On such large scales, the dynamic nature of spacetime itself would play an important role. Especially if, as evidence suggests, gravitational waves travel no faster than light.

jobigoud 8y ago

How is it the right order of magnitude? Did you compute that based on the size of the observable Universe? But that's arbitrary, the Universe is way bigger than that.

Simon_says 8y ago
No. The input into the equation is the density of matter in space, nothing having to do with the size of the observable universe. On large scales in the visible universe, matter is fairly evenly distributed at a density of about 1 atom of hydrogen per cubic meter. For any constant nonzero density form of matter, if you pack enough of it together in a sphere in a flat spacetime, its Schwarzchild radius will eventually exceed its radius. This is because the Schwarzchild radius is proportional to the mass, but the radius of the actual matter is proportional to the cube-root of the mass. It's a fun thought experiment, but not physically meaningful in this universe because our spacetime is expanding, and the original calculations assume there's nothing at the edge pulling 'outward', but in our universe there is.
- pdonis 8y ago
  > For any constant nonzero density form of matter, if you pack enough of it together in a sphere in a flat spacetime, its Schwarzchild radius will eventually exceed its radius. You can't do this in flat spacetime, because the matter curves spacetime, and the denser you pack it, the more it curves spacetime.
  - Simon_says 8y ago
    Obviously. The point of the thought experiment was that you start with a universe with no other matter in it that's not expanding, both of which conditions our universe violates.
- dantillberg 8y ago
  Thank you, you're adding more concrete verbiage to my suspicions that my calculations were too naive: I was only doing classical, pre-General-Relativity, calculations. On such large scales, the dynamic nature of spacetime itself would play an important role. Especially if, as evidence suggests, gravitational waves travel no faster than light.