In another thread 'Entropy, information and Omphalos cosmology' I commented on a strange fact (which I think many are aware of): namely that(adsbygoogle = window.adsbygoogle || []).push({});

to which there was an interesting reply: .... a black hole with the universe's mass has an event horizon with similar radius? It could then be argued that our flat universe is nothing but a black hole...

This subject seems to me not to have an immediate bearing on questions of entropy (or Omphalos cosmology, for that matter) and to deserve consideration on its own. Hence this new thread. When it comes to black holes, cosmology becomes quite "above my fireplace", and I can't be of much use. Moving Finger said:"The current estimate for average baryon density is about 10^-30 grams/cc. The mass-equivalent of photon density is about 4 orders of magnitude lower than this (therefore may be ignored). At this baryon density (assuming no dark matter), the universe would need (based on my calculations) to have a radius of approx 4 x 10^10 light years or more in order to be a black hole. The “observable” universe is I believe estimated at about 1.4 x 10^10 light years in radius? That does indeed seem very close to the size needed for being a black hole (especially when you factor in the estimate of dark matter density which may be many times more than the baryon density). But if the universe is a black hole, then how does this match up with the observation that the universe is expanding at an ever-increasing rate? Does this mean that at some time in the future the universe will stop being a black hole? Or does it just become an increasingly bigger and less dense black hole?

The critical black hole density scales (I believe) as the inverse square of the schwarzchild radius, so a doubling of radius would result in one quarter of the critical density. But for a given volume containing a fixed mass, doubling the radius would result in a drop in density to one eighth (actual density for a given mass scales as the inverse cube of the radius). Thus if the universe is today a black hole, and it continues expanding, it must (if it is finite in size) reach a point at some time in the future when it stops being a black hole.

It seems quite a coincidence that the present era corresponds to a density and size of universe which is just on the borderline of being a black hole…… go back to much earlier times (less than a billion years of age) and our universe was definitely a black hole, go forward to much later times (more than 100 billion years of age) and our universe is no longer a black hole. Is this right, or am I making some big mistakes somewhere?"

I make only one remark: perhaps it is dangerous to mix symmetries. The metric of a black hole is spherically symmetric, and static; the Robertson-Walker metric of the standard model universe depends on time and is isotropic everywhere. Could this produce strange results like those mentioned above?

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# Black holes and the expanding universe

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