Gravitational waves in general relativity XV. The loss-free case

Abstract

Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Bondi Sir Hermann 2000Gravitational waves in general relativity XV. The loss-free caseProc. R. Soc. Lond. A.4562645–2652http://doi.org/10.1098/rspa.2000.0630SectionRestricted accessResearch articleGravitational waves in general relativity XV. The loss-free case Sir Hermann Bondi Sir Hermann Bondi Churchill College, Cambridge CB3 0DS, UK Google Scholar Find this author on PubMed Search for more papers by this author Sir Hermann Bondi Sir Hermann Bondi Churchill College, Cambridge CB3 0DS, UK Google Scholar Find this author on PubMed Search for more papers by this author Published:08 November 2000https://doi.org/10.1098/rspa.2000.0630AbstractIn Maxwellian electrodynamics, the linearity of the theory permits the superposition of equal advanced and retarded waves. This results in the source of the radiation suffering no loss of energy. This paper aims to look at the applicability of this analysis to the theory of gravitation. Without loss of energy, such a system can be stationary. To study this situation, a slightly azimuth–dependent stationary rotating cylindrical system is examined in the vacuum outside the bounded source. It is shown that imposing time independence on the metric in a co–rotating frame leads to a 'critical circle' where the coordinates attain the speed of light. This divides space into an inner zone where the vacuum field equations are elliptic and an outer one where they are hyperbolic. Retaining the azimuth–dependent terms only to first order, the angular dependence can be Fourier analysed. For each Fourier component, a set of ordinary differential equations describes the field throughout empty space. This set links the inner zone surrounding the source with the outer (wave) zone. The asymptotic behaviour in the wave zone is studied and the inner zone is looked at for slowly rotating sources. The validity of the analysis is discussed and it is hoped that this approach will illuminate more realistic situations. Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited byBondi S (2004) Gravitational waves in general relativity XVI. Standing waves, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 460:2042, (463-470), Online publication date: 8-Feb-2004. Bi ák J, Ledvinka T, Schmidt B and ofka M (2004) Static fluid cylinders and their fields: global solutions, Classical and Quantum Gravity, 10.1088/0264-9381/21/6/019, 21:6, (1583-1608), Online publication date: 21-Mar-2004. Bic$aacute$k J and Zofka M (2002) Notes on static cylindrical shells, Classical and Quantum Gravity, 10.1088/0264-9381/19/14/307, 19:14, (3653-3664), Online publication date: 21-Jul-2002. This Issue08 November 2000Volume 456Issue 2003 Article InformationDOI:https://doi.org/10.1098/rspa.2000.0630Published by:Royal SocietyPrint ISSN:1364-5021Online ISSN:1471-2946History: Published online08/11/2000Published in print08/11/2000 License: Citations and impact Keywordsgravitational wavescylindrical systemshyperbolic equationsslight azimuth dependencerotating coordinatesstanding waves