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If i start from the Einstein Hilbert ACtion and apply the usual Noether rules (as we use them on flat spacetime ie treating the metric tensor g_munu as any other tensor assuming the existence of another hidden tensor eta_munu describing a flat spacetime non dynamical background, though the latter appears actually nowhere in the action which makes this approach appear quite metaphysical though it might make more sense if the true dynamical metric g_munu describes an asymptotically minkowskian spacetime)

Considering translations (the action is general covariant so also invariant under translations of course) the Noether current computing is expected to be tedious (in part because the Lagrangien involves second order derivatives) .... but i guess this has been done already a long time ago and my question is:

- can anyone confirm that i will get the GR pseudo tensor (the one used to compute the energy-momentum carried by GW) ?

the answer is difficult to find in most text book because there is a much easier way to introduce the pseudo energy-momentum tensor starting from the Einstein equation and making use of the linearised Bianchi identities...

So i need confirmation that the pseudo tensor is also the same that would be obtained by applying the Noether theorem.

Thank you in advance

Fred

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# GR Noether current

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