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Conformal coupling of gravitational wave field to curvature

Grishchuk, L. P. and Yudin, V. M. (1980) Conformal coupling of gravitational wave field to curvature. Journal of Mathematical Physics, 21 (5). pp. 1168-1175. ISSN 0022-2488. http://resolver.caltech.edu/CaltechAUTHORS:GRIjmp80

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Abstract

Conformal properties of the equations for weak gravitational waves in a curved space–time are investigated. The basic equations are derived in the linear approximation from Einstein's equations. They represent, in fact, the equations for the second-rank tensor field hαβ, restricted by the auxiliary conditions hαβ;α=0, h=γαβhαβ=0, and embedded into the background space–time with the metric tensor γαβ. It is shown that the equations for h are not conformally invariant under the transformations γαβ=e2σγαβ and hαβ=eσhhαβ, except for those metric rescalings which transform the Ricci scalar R of the original background space–time into e−2σR, where R is the Ricci scalar of the conformally related background space–time. The general form of the equations for hαβ which are conformally invariant have been deduced. It is shown that these equations cannot be derived in the linear approximation from any tensor equations which generalize the Einstein equations.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1063/1.524541DOIUNSPECIFIED
Additional Information:© 1980 American Institute of Physics. Received 20 November 1979; accepted for publication 7 December 1979. Supported in part by the Ministry of Higher Education, USSR, and by the National Science Foundation, USA (AST76-80801 A02). Thanks are due to B. Mashhoon for reading the manuscript.
Funders:
Funding AgencyGrant Number
Ministry of Higher Education (USSR)UNSPECIFIED
National Science FoundationAST76-80801 A02
Subject Keywords:EINSTEIN FIELD EQUATIONS, GRAVITATIONAL WAVES, SPACE-TIME, RICCI TENSOR, CONFORMAL INVARIANCE
Record Number:CaltechAUTHORS:GRIjmp80
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:GRIjmp80
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:12051
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:24 Oct 2008 06:29
Last Modified:26 Dec 2012 10:26

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