A Note on General Relativity, Energy Conservation, and Noether’s Theorems

The subject of this note has been a small historical thread in the long and complex story of the status of energy conservation in General Relativity, concerning two related claims made by Klein and Hilbert: that the energy conservation law is an identity in generally covariant theories, and that this marks a contrast with other (earlier) theories. Both these claims were disputed by Einstein. We have seen how three theorems proved by Noether and Klein can be brought to bear on this disagreement, showing that: