Einstein's vacuum equations, that is without matter, allows the possibility of curvature without matter. For instance, we may consider gravitational waves.
The question is: Is there some link between the Riemann curvature tensor, and/or the Weyl tensor, and some gravitational "physical" quantities (as stress-energy tensor or total energy)?
Of course, at first glance, there is no covariant gravitational stress-energy tensor, so it seems there is no relation, but maybe things are more subtle?