Conserved currents, superpotentials and cosmological perturbations

Abstract

Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Petrov Alexander N. and Katz Joseph 2002Conserved currents, superpotentials and cosmological perturbationsProc. R. Soc. Lond. A.458319–337http://doi.org/10.1098/rspa.2001.0865SectionRestricted accessConserved currents, superpotentials and cosmological perturbations Alexander N. Petrov Alexander N. Petrov Sternberg Astronomical Institute, Universitetskii prospect 13, Moscow 119899, Russia (, ) Google Scholar Find this author on PubMed Search for more papers by this author and Joseph Katz Joseph Katz The Racah Institute of Physics, 91904 Jerusalem, Israel () Google Scholar Find this author on PubMed Search for more papers by this author Alexander N. Petrov Alexander N. Petrov Sternberg Astronomical Institute, Universitetskii prospect 13, Moscow 119899, Russia (, ) Google Scholar Find this author on PubMed Search for more papers by this author and Joseph Katz Joseph Katz The Racah Institute of Physics, 91904 Jerusalem, Israel () Google Scholar Find this author on PubMed Search for more papers by this author Published:04 January 2002https://doi.org/10.1098/rspa.2001.0865AbstractConserved vectors are divergencies of superpotentials. In field theory on curved backgrounds, they are useful in calculating global ‘charges’ in arbitrary coordinates and local conserved quantities for small perturbations with specific gauge conditions. Superpotentials are, however, ill–defined. A new criterion of Julia and Silva selects uniquely for Dirichlet boundary conditions the ‘KBL superpotential’ as proposed by Katz, Bičák and Lynden–Bell, which has remarkable properties.Here, we show that a Belinfante–type addition to the KBL superpotential in general relativity gives an expression that is independent of boundary conditions defined by a variational principle. The modified superpotential has the same global properties as the KBL one, except for angular momentum at null infinity, and it does not differ from the KBL superpotential in the linearized theory of gravitation.As an illustration in linearized theory on curved backgrounds, we calculate conserved quantities for small perturbations on a Friedmann–Robertson–Walker spacetime associated with conformal Killing vectors. Our unifying view relates a number of applications in cosmology found in the literature. Globally conserved quantities have simple physical interpretations in the ‘uniform Hubble expansion’ gauge. Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Oltean M, Moghaddam H and Epp R (2021) Energy of cosmological spacetimes and perturbations: a quasilocal approach * , Classical and Quantum Gravity, 10.1088/1361-6382/abeae3, 38:8, (085012), Online publication date: 22-Apr-2021. Petrov A (2019) Field-theoretical construction of currents and superpotentials in Lovelock gravity, Classical and Quantum Gravity, 10.1088/1361-6382/ab516d, 36:23, (235021), Online publication date: 5-Dec-2019. Feng J (2018) Some globally conserved currents from generalized Killing vectors and scalar test fields, Physical Review D, 10.1103/PhysRevD.98.104035, 98:10 Chen C, Liu J and Nester J (2018) Quasi-local energy from a Minkowski reference, General Relativity and Gravitation, 10.1007/s10714-018-2484-z, 50:12, Online publication date: 1-Dec-2018. 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Ilin R and Paston S (2020) Energy–Momentum Pseudotensor and Superpotential for Generally Covariant Theories of Gravity of General Form, Universe, 10.3390/universe6100173, 6:10, (173) Pitts J (2020) General Relativity, Mental Causation, and Energy Conservation, Erkenntnis, 10.1007/s10670-020-00284-7 This Issue08 February 2002Volume 458Issue 2018 Article InformationDOI:https://doi.org/10.1098/rspa.2001.0865Published by:Royal SocietyPrint ISSN:1364-5021Online ISSN:1471-2946History: Published online04/01/2002Published in print08/02/2002 License: Citations and impact Keywordsgeneral relativitysuperpotentialsconservation lawscosmological perturbations