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This seems at first to be easy, but it is not clear that it is. The stress energy pseudo-tensors of the gravitational field are constructed solely such that the divergence of the sum of {the gravitational field stress-energy pseudo-tensor plus the stress-energy of matter} is zero. I am not sure the standard gravitational field pseudo-tensors ones will work on this procedure in the gauge that is used.

It was Weinberg that did this. If anyone can provide me with the Weinberg reference I would be very grateful.