🚀 go-pugleaf

About pg 739 of MTW (a discrete grid-universe)...

I admit I fail to see why the `geometry in a cell'
(around each grid-point) must be Schwarzschild,
because of some succesfull approximation in solid-
state (!) physics. Each cell completely isolated from
the influence of the other grid-points or what?

I would love to see a rigorous proof of the assertion
that the Schwarzschild-cell-geometries `match up smoothly'
at the boundaries between cells (that would mean a
beautiful new solution of Einstein's equations; so
nice of MTW to leave that discovery to the eager reader).
But most of all, I would like to see some serious definitions
instead of that sloppy picture.

Just to show where sloppiness can lead to, consider
the grid in a compact hyperbolic universe (angle-deficit
for the sum of observed angles in a triangle consisting
of 3 grid-points, instead of angle-excess, as automatically
assumed by MTW). Follow MTW's argument once more, and
come out with the conclusion that a hyperbolic universe
eventually recontracts.

Now how is that for an `agreement to 4% or better' with
the standard perfect-fluid model?

I repeat my claim (of the former thread `Hubble-constant')
that there is no proof whatsoever that a discrete grid-
universe behaves the same as a perfect fluid universe
with the same mean density.

marc van loo.