One of the reasons General Relativity (GR) has been so hard to test is that its very hard to find or set up conditions where its predictions differ from those of Newton's laws. That's why the first case of the observed bending of light in a gravitational field was such a big deal.
One predicted effect of GR is that a lump of spinning matter will tend to drag space-time along with it. This is known as the "dragging of inertial frames".
It takes a lot of mass spinning really fast to amount to anything we can observe, and black holes or neutron stars will be the best places to look for it.
Now, it looks like astronomers are finding it. Fluctuations in x-ray levels as matter falls into black holes appear to match the fluctuations we'd see if space-time was rippling around a black hole.
That Einstein was a pretty smart guy.
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