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Q & A: Schwarzschild universe?

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Q:
I calculated that Schwarzschild radius of the black hole with the mass of visible universe is equal to the radius of the visible universe (13E9 ly). Is it random coincidence or does it result from some theory?
- Ladislav Viererbl (age 57)
Czech Rep.
A:
What a great question! It's no coincidence.

I'm going to treat this equality only to an approximate degree (say a factor of 3 or so) , because I'm not familiar with the precise calculation, or even sure what coordinate system you're using. 

First, let me help other readers catch up with you. The Schwarzschild  radius of a black hole is the radius at which the escape velocity equals the speed of light, c. You can calculate it approximately using standard Newtonian gravity, getting about GM/c2, where G is the universal gravitational constant, and M is the mass of the black hole. (Specialists will note that I've dropped a factor of 2.)

Since the universe has been expanding at an approximately constant rate since shortly after the Big Bang, 13.7 bil years ago, the most distant 'observable' parts are 13.7 bil light-years away. Saying that the Schwarzschild radius calculated from the mass in that region is the same as the actual radius is equivalent to saying that the universe is very nearly expanding at 'escape velocity', i.e. that the amount of mass in it is about what's needed to cause it to re-contract.

We should be clear that there are two kinds of mass (or, equivalently, energy) around. One is ordinary mass, whose density drops as the universe expands, and whose gravity tends to pull the universe together. This currently accounts for about 30% of the total energy. The other is a background "dark energy", whose density stays constant (or nearly so) as the universe expands, and whose gravity must therefore, according to General Relativity, push the universe apart. About 70% of the energy is this latter kind.

So now we get to your question: why would we have anything like an equality between that 13.7 bil light years and GM/c2 for either the ordinary mass or the total mass-energy? There are two stages to the answer, neither completely clear-cut.

The first is that some process in the early universe caused it to be extremely near to 'flat', which makes your equation work, at least with the right numerical prefactor, when you include both ordinary mass and the dark energy in "M". The standard view is that  the process was rapid inflation, an exponential expansion that results when the background energy density is large. The reasons for the large early energy density are the subject of active speculation. An alternative view, tentatively supported by some subtle observations,  is that the universe started off flat, with the Bang being a collision between two such flat 'branes'.  At any rate, there seems to be some basic reason why the universe is very nearly flat.

That brings us to stage two: why is the density of mass in the universe some appreciable fraction of the total energy density? Why isn't it 0.000000001 of the total, with .999999999 in the background? 0r 3000 times the total, with -2999 in the background? Here's where life gets interesting. If the mass density were much higher, the universe would have long since re-collapsed, and nobody would have evolved to ask such good questions. If the mass density were much less, nothing would clump up enough to make the stars and then elements needed for life, so again, nobody would be asking.

It looks as if the background dark energy were 'tuned' to just the right density so that the remaining mass density needed to make the universe flat would be in the narrow range that could support life.  Why would that be? Again, we don't know, but perhaps the best guess is that some huge number of different possible background densities, allowed by string theory, all occur. In the universes where the wrong ones occurred, nobody is asking why. An excellent book on this topic is "The Cosmic Landscape", by Lenny Susskind.

Mike W.

(published on 03/19/09)

Follow-Up #1: are we the other side of a black hole?

Q:
According to some calculations that I have made, it seems that the universe we know is in fact a black hole. If we use the radius of the observable universe as 6.62251133080656x10e22 km and the mass as 3.35x10e54 kg (source http://en.wikipedia.org/wiki/Observable_universe#Estimation_based_on_critical_density) as values for the calculation of gravitational acceleration and of escape velocity, we get these results : 5.1x10e-8 m/sec2 and 2598533 km/s. Since the result for escape velocity is greater than the speed of light, it seems that we are inside a black hole; we cannot escape the gravitational pull of the entire universe. I know that I didn't consider dark matter. But the conclusion that I can draw of these results is that maybe, the Big Bang came from a black hole in another universe. And maybe our black holes create other universes. What do you guys think?
- Anonymous
A:
I should warn you that for the most part questions like this are over my head.

First, I've marked this as a follow-up to a previous question on the mass and size of the universe. In that we explain what the known and suspected constraints are on that density-size relation. The sort of bare flat-space Newtonian calculation that you give for the escape velocity cannot work, however. For a homogeneous universe the average gravitational field is everywhere about zero, by symmetry. However, the black-hole-like numbers are no coincidence, whatever the origin of our universe might be, as we explain.

Now as to whether we are essentially the white-hole side of a black-hole white-hole bridge, that idea has been put forth in refereed publications (see below)  which I am not qualified to evaluate. It is only one of many ideas of how our universe's spacetime might be embedded in a more complete and complicated  manifold.

Mike W.

Physics Letters B     Volume 687, Issues 2-3, 12 April 2010, Pages 110-113

Radial motion into an Einstein—Rosen bridge

Nikodem J. Popławski

Abstract.... our own Universe may be the interior of a black hole existing inside another universe.


(published on 12/25/10)

Follow-up on this answer.