[hither_shores]

No, it really is possible to violate momentum conservation in suitably curved spacetimes. But this is a straightforward consequence of the laws of physics, not a "defiance" of them: it falls right out of general relativity. We still have a conservation law for the stress energy tensor, given by ∇_{μ}T^{μν}=0, it just doesn't give rise to separate global conservation laws on each component.

The same applies to the system they actually built, except that the nonconserved "momentum" is not the same as the usual notion. It's the conjugate momentum(https://en.wikipedia.org/wiki/Canonical_coordinates) for the coordinates on the surface.

[pmayrgundter]

Ok, interesting.

In the system you describe, is it possible for the center of gravity of an isolated system to move without ejecting mass or light?

[hilbert42]

What you say seems to make sense to me. Even if we understand the math of GR we've often still difficulties in interpreting the practicalities of it.

Besides, whenever we see statements about defying the laws of physics our immediate reaction should be to look deeper. Say, if some action seems to defy Newton then look to SR thence GR for the reason.