1999/05/22 by A. N. Petrov, J. Katz
Physics and Astronomy · #gr-qc
published as Fundamental Interaction: From Symmetries to Black Holes (eds.: J.M. Frere, M. Henneaux, A. Servin & Ph. Spindel), p.p. 147-157. Brussels: Universite Libre de Bruxells (1999). · 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
arxiv created 1999/05/22 · arxiv updated 2009/11/30
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.