Gravitational energy is non-local which is essentially because of the equivalence principle. The equivalence principle says that you can always transform your frame so that you feel like in a Minkowski space-time locally. Mathematically, there is no tensor-like definition for gravitational energy in General Relativity. All energy-momentum tensor for gravitational energy must be pseudo-tensor, namely frame-dependent tensor. About the non-locality of gravitational energy I have two questions:
- Where does the energy of gravitational waves come from which seems way local?
- How can the non-locality of gravitational energy be implemented in String theory where, for example, gravitons are simply zero modes of closed strings and strings are explicitly local (of course except for the resolution of strings which, as I see, is different from the non-locality of gravitational energy)?