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*From*: "Paul Camp" <pjcamp@coastal.edu>*Date*: Mon, 17 Feb 1997 13:29:19 EST

Regarding:

A black hole needs a "universe" to be in (spacetime and all that good

stuff). It is not at all clear what the environment that preceded the

big bang consisted of? Could it be characterized by a spacetime

dimensionality? A temperature? A vacuum?

Perhaps the Big Bang occurred everywhere simultaneously, so it wouldn't need

a location. Does that constitute too large a leap of faith?

JFK

It is not too large since that is exactly what happened. The

universal expansion should not be thought of as stuff flying out into

a previously existing spacetime. Rather, the spacetime has always

been full of stuff, the spacetime geometry is what is doing the

changing, and the stuff is largely just along for the ride. All this

follows from the isotropy assumptions built into most Big Bang

models.

Regarding the black hole equivalence, that only works if the overall

geometry of the universe is closed. All radial geodesics then form closed

loops or terminate on a singularity -- i.e., you can't get out,

which is really all that is required of the interior solution for a

black hole (quantum phenomena excluded, of course). In particular, it

does not necessarily have to be embedded in a larger geometry -- you

don't have to have an outside in order to have an inside. And in

both cases, the classical singularity lies in a timelike direction.

None of this holds at all in flat or open geometries.

It is not too hard to show that as the radius of a black hole's event

horizon becomes larger and larger, corresponding to ever larger

masses, the average density becomes less and less. You could then

easily mock up a black hole solution with a density equal to that of

the universe with the condition that it hasn't yet all fallen into

a singularity. Of course, the main problem with all of this is that

nobody really knows what the "correct" interior solution is for a

black hole and in fact you can get a great deal of argument on

exactly that point. However, in terms of the geodesic structure, it

is pretty nearly the same as a closed universe so there is at least a

logical equivalence. What got the expansion started is purely a

matter of conjecture and, since all inlfationary models require the

universe to be pretty much flat anyway (and therefore decidedly

un-black-hole-like) it is probably a moot point.

Paul J. Camp "The Beauty of the Universe

Assistant Professor of Physics consists not only of unity

Coastal Carolina University in variety but also of

Conway, SC 29528 variety in unity.

pjcamp@coastal.edu --Umberto Eco

pjcamp@postoffice.worldnet.att.net The Name of the Rose

(803)349-2227

fax: (803)349-2926

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