Re: Possibly a Stupid Question...
The equations of GR have, essentially, matter on one side (in fact energy-momentum, which includes matter, radiation &c) and spacetime curvature on the other. So yes, they do strongly constrain the spacetime curvature in the absence of matter. Spacetime certainly can not contain arbitrary ripples or wrinkles, as you claim. However it's also not the case that all vacuum solutions (which is what such solutions are called) must be flat: there are a bunch of different families of them, including, for instance, the Schwarzschild solution and lots of things including gravitational waves. None of these make much sense as a way of explaining dark matter.
(The flip side of this is dark energy, and GR has no problem there: dark energy just appears as a 'cosmological constant' which was initially present in the equations, then removed by Einstein for reasons which turned out not to be very good, and has now been put back. The cosmological constant only explains certain sorts of dark energy and I don't know if what we observe agrees with what GR predicts although I think it does. There remains the problem of trying to understand why it has the value it does, and I think that's a problem.)
Biting the hand that feeds IT
