Since gravitational wave spacetimes are time-varying vacuum solutions ofEinstein's field equations, there is no unambiguous means to define theirenergy content. However, Weber and Wheeler had demonstrated that they do impartenergy to test particles. There have been various proposals to define theenergy content but they have not met with great success. Here we propose adefinition using "slightly broken" Noether symmetries. We check whether thisdefinition is physically acceptable. The procedure adopted is to appeal to"approximate symmetries" as defined in Lie analysis and use them in the limitof the exact symmetry holding. A problem is noted with the use of the proposalfor plane-fronted gravitational waves. To attain a better understanding of theimplications of this proposal we also use an artificially constructedtime-varying non-vacuum metric and evaluate its Weyl and stress-energy tensorsso as to obtain the gravitational and matter components separately and comparethem with the energy content obtained by our proposal. The procedure is alsoused for cylindrical gravitational wave solutions. The usefulness of thedefinition is demonstrated by the fact that it leads to a result on whethergravitational waves suffer self-damping.
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