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Conservation Laws for Large Perturbations on Curved Backgrounds

A. N. Petrov·J. Katz
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Abstract

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 Noether's theorem combined with Belinfante's "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.

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A. N. Petrov, J. Katz. 1999-05-22. Conservation Laws for Large Perturbations on Curved Backgrounds. https://arxiv.org/abs/gr-qc/9905088

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