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Conserved currents, superpotentials and cosmological perturbations
2002
Proceedings of the Royal Society A
We first consider the Lagrangian formulation of general relativity for perturbations with respect to a background spacetime. We show that by combining Noether's method with Belinfante's "symmetrization" procedure we obtain conserved vectors that are independent of any divergence added to the perturbed Hilbert Lagrangian. We also show that the corresponding perturbed energy- momentum tensor is symmetrical and divergenceless but only on backgrounds that are "Einstein spaces" in the sense of A.Z.
doi:10.1098/rspa.2001.0865
fatcat:b5lqr4c3dvdhnf2uwhvrh2d32a