Conservation Laws for Large Perturbations on Curved Backgrounds
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.
Keywords
Cite
@article{arxiv.gr-qc/9905088,
title = {Conservation Laws for Large Perturbations on Curved Backgrounds},
author = {A. N. Petrov and J. Katz},
journal= {arXiv preprint arXiv:gr-qc/9905088},
year = {2007}
}
Comments
13 pages, LaTeX, to appear in the Proceedings of the Conference on "Fundamental Interactions: From Symmetries to Black Holes" held in Brussels March 25 - 27, 1999