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From: wkp@lanl.ARPA
Newsgroups: net.physics
Subject: Re: Big Bang Impossible
Message-ID: <17915@lanl.ARPA>
Date: Wed, 12-Dec-84 22:47:21 EST
Article-I.D.: lanl.17915
Posted: Wed Dec 12 22:47:21 1984
Date-Received: Sun, 16-Dec-84 06:38:30 EST
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Organization: Los Alamos National Laboratory
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>>> If the whole universe was in a speck, said spec would have been a black hole
>>> and the "big bang" could not happen.  No one has yet disputed this. Why not?

>> [me:]
>> The answer is that the matter in your speck never crossed the "event
>> horizon" of the universe, i.e., it never escaped from the black hole........

>  [Sharp replies:]
> Oh dear me no !  Over and over again I see this confusion.  The Universe is
> NOT, was NOT, and NEVER CAN BE, a black hole.  Why ? I hear you scream.
> Because a black hole has an asymptotically flat spacetime around it, and the
> Universe has nothing around it (in fact, not even nothing).
> A black hole is only defined in terms of the spacetime around it, whilst the
> Universe is defined purely internally.  The reason for the apparent
> coincidence that the mass of the Universe at which it is just closed
> and the apparent radius of the Universe obey the same relation as the mass
> and radius of a black hole, is that they are both governed by Einstein's
> equations.  In fact, if you're still not convinced, look at it this way:
> if the Universe is just closed, then it's gravitational energy balances
> it's kinetic energy of expansion.  Thus, the net energy of the Universe
> is zero - and since it's the total mass-energy which enters into the
> black hole formula, it's clearly wrong.
> -- 
> 	Nigel Sharp   [noao!sharp  National Optical Astronomy Observatories]

[I reply in utter frustration:]

Bogus, bogus, bogus, bogus, bogus!  Off the scale on the bogus meter!
Come on, Nigel, I'm sure they didn't teach you to obfuscate the issues 
like that in Her Majesty's schools.

Let me remind you of the original question:  how could mass be blown
off the extremely massive speck which contained all the mass in the
universe.  This is a classical problem, and can be solved without any
recourse to Einsten's equations.  This may be a sore point with 
those who prefer to define black holes in a purely formal way, i.e.,
by defining them as certain highly-specialized exact solutions
of Einstein's equations [e.g., see McVittie's article in the
British journal _The Observatory_ vol. 98, p. 272 (1978).]  If all
you're saying is that a big-bang universe is not described by
a solution to Einstein's equation because the asymptotic space-time
boundary condition is undefined, you are correct.

However, let's answer the question, shall we?  As Laplace himself
solved this problem [see Hawking & Ellis's book on the large scale
structure of space-time] I am quite confident of the solution, and I
trust you are too.  In any case, if all the mass of the universe was  
centered in a speck, the absolute limiting distance that a particle
with velocity c can traverse is R=2GM/(c**2).  As long as it is within
this distance, no physical laws are violated, which accounts for the
fact that this is * n o t * an inconsistency in the Big Bang theory.


					   bill peter
					   los alamos