RE: Big Bang from Big Black Hole

["Paul Camp" <pjcamp@coastal.edu>]

> 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
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