Conservation Laws for Large Perturbations on Curved Backgrounds

Backgrounds are pervasive in almost every application of general relativity. Here we consider the Lagrangian formulation of general relativity for large perturbations with respect to a curved background spacetime. We show that Noethers theorem combined with Belinfantes symmetrization method applied to the group of displacements provide a conserved vector, a superpotential and a energy-momentum that are independent of any divergence added to the Hilbert Lagrangian of the perturbations. The energy-momentum is symmetrical and divergenceless only on backgrounds that are Einstein spaces in the sense of A.Z.Petrov.