Re: big-bang energetics

[John Denker <jsd@MONMOUTH.COM>]

At 12:56 AM 8/21/99 -0400, David Bowman wrote:
>  Global energy
> conservation is not guaranteed (or even objectively definable) in GR--
> especially for a metric that is (a) everywhere time dependent, and (b)
> not asymptotic to a flat Minkowski metric at 'infinity' for a universe
> that has an always a localized distribution of matter.  Unfortunately,
> the usual Friedmann-Robertson-Walker metric models for the big bang
> satisfy neither a) nor b).

That's interesting.

> As usual with city politics and GR
> everything is local.  Energy is locally conserved in that its density
> obeys a relativistic continuity equation.

Good.  That makes the rest of the novel things you say infinitely less
shocking.

> But this
> local conservation law does not always translate into a global
> conservation or even coordinate system-independent definability of the
> very concept.

OK. I don't see why anybody needs to worry about global conservation.  I'm
not even 100% sure what that would mean.  The universe is a big place.

You've said there is a local continuity equation, which I assume is a
differential equation which in pedestrian 3+1 coordinates would be roughly
        - d stuff / d t = div flux

So my question concerns *regional* conservation.  Can I construct a pillbox
and apply Gauss's law to get a regional integral form of the conservation
law, or is the early geometry to messed up to permit that?

(Thanks for your many thoughtful and thought-provoking posts.)