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From: jlg@lanl.ARPA
Newsgroups: net.physics
Subject: Re: Big Bang Impossible
Message-ID: <17768@lanl.ARPA>
Date: Mon, 10-Dec-84 16:07:19 EST
Article-I.D.: lanl.17768
Posted: Mon Dec 10 16:07:19 1984
Date-Received: Thu, 13-Dec-84 01:41:16 EST
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Organization: Los Alamos National Laboratory
Lines: 47

> If the whole universe was ina speck, said spec would have been a black hole
> and the "big bang" could not happen.  No one has yet disputed this. Why not?

The whole universe was not (necessarily) in a spec.  The density of the 
universe was very high.  All of the universe that is presently visible
(radius of about 15 billion light-years now) was once compressed into a VERY
small space.  However, high density does not cause black holes - high
gravitational curvature does.  

Let's take a few examples:

1) Assume an infinite universe with uniform, but very high, density.  Since
   the universe is infinite, it is radially symmetric around any point. Any
   radially symmertic region has a gravitational field of zero in the interior
   of the region (any physics 200 level course will force you to work out 
   infinite variations on the proof of this fact for any inverse-square force
   ad nauseum).  Therefore the gravitational curvature within this universe 
   is zero everywhere - regardless of the density.  (Now start stretching
   this universe uniformly in all directions and you'll have a 'big-bang'
   effect.)

2) Assume a finite, unbounded universe with uniform, but very high, density.
   Since it's hard for most people to visualize such a thing, consider the
   surface of a sphere.  The surface of the sphere is radially symmetric 
   around any point.  A sphere's surface is a two dimensional object which
   is curved in the third dimension; the three dimensional analog of this
   curved in the fourth dimension is an example of a finite, unbounded space.
   As on the sphere, the 'hypershpere' is radially symmetric around every
   point, and by argument (1), the gravitational curvature is everywhere zero.
   (Now expand this universe uniformly in every direction, like increasing
   the diameter of the shere, and you again have a 'big-bang' effect.)

3) Assume either an infinite or finite universe that is at least VERY LARGE
   (this means at least large enough for the following scenario).  Assume
   that the density is not uniform, but is VERY high in one region and
   low elsewhere.  If the density of this universe declines gradually as
   function of the distance from the center of the high density region, so
   gradually that the gravitational curvature nowhere exceeds the Swartzchild
   limit, then no black hole will form.  Since the properties of such VERY
   dense matter are not well known, this dense region may start to expand 
   into the surrounding space (due perhaps to nothing more complicated than
   pressure).

Well, there are three possibilities.  None of these imply a primordial
black hole, and all of them lead to the possibility of an expanding universe.
Which of these (if any) is accurate is a subject for controversy, and there
may be other explanations which are just as good.