In article ,
Tobias Fritz wrote:

Lee Smolin told me some neat stuff about MOND - that's "Modified
Newtonian Dynamics", which is Mordehai Milgrom's way of trying to explain
the strange behavior of galaxies without invoking dark matter. The basic
problem with galaxies is that the outer parts rotate faster than they
should given how much mass we actually see.

Doesn't it seem unreasonable to discard a theory as successful as GR?

Of course! I don't think anyone wants to discard GR because of the
dark matter problems. But, it does make sense to have some people
play around with other ideas.

Except for a few partisans, nobody will take MOND seriously until
it's extended to a full-fledged theory that matches the successes of
GR and isn't horribly ugly - or until it makes some prediction that's
almost impossible to match using conventional means (e.g. fine-tuned
dark matter).

But, it's still good to look at the rotation curves in the paper I
referred to, and wonder what's really going on!

Or is it somehow possible to fit MOND into the framework of GR, like by
modifying the field equations, perhaps by including torsion?

People are trying very hard to fit MOND into GR in all possible ways,
and also to design dark matter that mimics the predictions of MOND.
Bekenstein's new paper:

Jacob D. Bekenstein
Relativistic gravitation theory for the MOND paradigm
http://www.arXiv.org/abs/astro-ph/0403694

seems like the best attempt so far to make MOND into a respectable
theory. It's still not elegant.

Everybody is talking about "dark matter" or alternative theories, when it is
not even really clear what the predictions of GR a recently I heard a
talk about the "averaging problem" in GR; basically, the message was that
we do not know if it is valid to take an average energy-momentum-tensor,
put it into the field equations and see the result as an average metric.

It's a nonlinear equation, so of course this is only approximately right
at best. The question is: is the approximation good enough for practical
purposes?

Unless there's strong evidence that the approximation is *not* good enough,
I think it's a bit over-sensational to say "it's not even really clear what
the predictions of GR are". In every application of fundamental theories
of physics to real-world problems, people make approximations. Trying to
rigorously justify these approximations leads to difficult and interesting
problems in mathematical physics. But, we rarely claim that it's not clear
what the theory actually predicts until we have made everything rigorous!
So, claiming this here might fool nonexperts into thinking there's a big
problem with general relativity, when it's actually just "life as usual".

By googling, I found the following paper:

http://arxiv.org/abs/gr-qc/9703016

which also has some references.

What do the experts think?

I think someone, e.g. the author of this paper, should do some
back-of-the-envelope calculations to guess how much error is introduced
into astrophysical or cosmological calculations by means of this
averaging approximation. If it's a lot, this is a subject of real
importance in astronomy. If it's a little, this subject will mainly
be interesting to mathematical physicists.

I can't imagine this "averaging problem" is big enough to explain the
effects that made people resort to dark matter and MOND, for example!

It might be relevant to understanding the details of hypernovae,
though: you've got a lot of dense matter moving around at relativistic
speeds, maybe turbulent, getting ready to collapse into a black hole...