Space-time curvature

Today I had an interesting discussion with Andrei
Gruzinov about space-time curvature. I
see clearly now that most of the un-intuitive aspects of
GR (even black holes) have the same source as the
un-intuitive aspects of special relativity. The fact that light
needs no medium for propagation leads to SR, and there
is little conceptually new in GR other than the equivalence
principle. The difference between SR and GR comes from the
fact that accelerations due to sources (such as gravity, EM)
have spatial gradients and this manifests itself as curvature
when you write down the covariant formulation.

There are some aspects of GR that seem really new, for
example the expansion of space. Andrei pointed
out that for an infinite universe you can always reformulate
the problem as particles in space given initial velocities flying
apart; nothing new there. But I don't think a closed universe
with positive curvature can be reformulated in that way
because it is not simply connected, so eventually the particles
will mix and this will produce observational differences.
The thing is, GR is a local theory, it doesn't tell us anything
about the global properties of the universe. We may
need something new altogether to address whether, for
example, the universe can have non-trivial topology.

Erin