Conservation Laws for Large Perturbations on Curved Backgrounds

Details Conservation Laws for Large Perturbations on Curved Backgrounds Conservation Laws for Large Perturbations on Curved Backgrounds

1999-05-22

arxiv.org/abs/gr-qc/9905088v1

Fundamental Interaction: From Symmetries to Black Holes (eds.: J.M. Frere, M. Henneaux, A. Servin & Ph. Spindel), p.p. 147-157

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages, LaTeX, to appear in the Proceedings of the Conference on "Fundamental Interactions: From Symmetries to Black Holes"

Scientific paper

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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