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RE: Big Bang from Big Black Hole


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?

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

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. --Umberto Eco The Name of the Rose
fax: (803)349-2926