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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 one question:

  1. Where does the energy of gravitational waves come from which seems way local?
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  • $\begingroup$ I don't think the energy density of gravitational waves is any less observer-dependent than the energy-density of electromagnetic waves. If string theory is a Lorentz-invariant theory, then it should reflect this fact. $\endgroup$ – CuriousOne Mar 1 '16 at 10:45
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    $\begingroup$ First one: I think usually for gravitational waves one defines a certain region in space D which is much larger than the wavelength of a gravitational wave: $D>>\lambda$ but at the same time define a region S which is much larger than D: $S>>D>>\lambda$. This way, one can define an average quantity for energy in the area D over some time scale and we can call it energy. The reason they do this is because for a local region (1 point) you can always transform back to minkowski metric. I guess you can have some 'energy' from the geodesic deviation equation as well (looking at oscillating masses) $\endgroup$ – Otto Mar 1 '16 at 11:37
  • $\begingroup$ Can't help with the second point :/ $\endgroup$ – Otto Mar 1 '16 at 11:38
  • $\begingroup$ Hi @Wein Eld: I removed the string theory question. Please only ask one question per post, cf. this meta post. $\endgroup$ – Qmechanic Mar 1 '16 at 12:12
  • $\begingroup$ @Otto Thanks for your comment. It seems that gravitational wave energy is not that local as I thought. It is like the tidal energy which is essentially non-local while looks like local? $\endgroup$ – Wein Eld Mar 1 '16 at 14:16

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