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• W2156125199 endingPage "5969" @default.
• W2156125199 startingPage "5957" @default.
• W2156125199 abstract "For every mapping of a perturbed spacetime onto a background and with any vector field ensuremath{xi} we construct a strongly, identically conserved covariant vector density $I(ensuremath{xi}),$ which is the divergence of a covariant antisymmetric tensor density, a ``superpotential.'' $I(ensuremath{xi})$ is linear in the energy-momentum tensor perturbations of matter, which may be large; $I(ensuremath{xi})$ does not contain the second order derivatives of the perturbed metric. The superpotential is identically zero when perturbations are absent. By integrating strongly conserved vectors over a part ensuremath{Sigma} of a hypersurface $S$ of the background, which spans a two-surface ensuremath{partial}ensuremath{Sigma}, we obtain integral relations between, on the one hand, initial data of the perturbed metric components and the energy-momentum perturbations on ensuremath{Sigma} and, on the other, the boundary values on ensuremath{partial}ensuremath{Sigma}. We show that there are as many such integral relations as there are different mappings, ensuremath{xi}'s, ensuremath{Sigma}'s, and ensuremath{partial}ensuremath{Sigma}'s. For given boundary values on ensuremath{partial}ensuremath{Sigma}, the integral relations may be interpreted as integral constraints on local initial data including the energy-momentum perturbations. Strong conservation laws expressed in terms of Killing fields $overline{ensuremath{xi}}$ of the background become ``physical'' conservation laws. In cosmology, to each mapping of the time axis of a Robertson-Walker space on a de Sitter space with the same spatial topology there correspond ten conservation laws. The conformal mapping leads to a straightforward generalization of conservation laws in flat spacetimes. Other mappings are also considered. Traschen's ``integral constraints'' for linearized spatially localized perturbations of the energy-momentum tensor are examples of conservation laws with peculiar ensuremath{xi} vectors whose equations are rederived here. In Robertson-Walker spacetimes, the ``integral constraint vectors'' are the Killing vectors of a de Sitter background for a special mapping." @default.
• W2156125199 created "2016-06-24" @default.
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• W2156125199 date "1997-05-15" @default.
• W2156125199 modified "2023-10-18" @default.
• W2156125199 title "Relativistic conservation laws and integral constraints for large cosmological perturbations" @default.
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• W2156125199 doi "https://doi.org/10.1103/physrevd.55.5957" @default.
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