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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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.
|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.|
|Subject Keywords:||EINSTEIN FIELD EQUATIONS, GRAVITATIONAL WAVES, SPACE-TIME, RICCI TENSOR, CONFORMAL INVARIANCE|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||24 Oct 2008 06:29|
|Last Modified:||26 Dec 2012 10:26|
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