Steve Carlip, on sci.physics.research has asserted that energy is not well defined. Paraphrasing him, if you want to have a concept of energy, you need to include gravitational potential energy, right? But you can always switch to a freely falling coordinate system in which gravitational potential is zero. And a tensor, if zero in any coordinate system is zero in every coordinate system. So since this is true at every point of spacetime, either energy is identically zero everywhere, or else it is not well defined, because only tensors are well defined (covariant) in GR. Exploring alternatives, Carlip suggests various physical possibilities that would generate meaningful energy definitions - it boils down to considering cases where physics breaks covariance, and the flat universe is the best bet here. The other alternative is that energy in GR could be NONLOCAL. If energy can only be defined within open sets, but not at points, the covariance argument fails. To me this suggests Bologiubov's definition of the quantum potential (which critically involved smearing over an open set in spacetime). Maybe some path like this could be explored?