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The Efroimsky perturbation scheme for consistent treatment of gravitationalwaves and their influence on the background is summarized and compared withclassical Isaacson's high-frequency approach. We demonstrate that the Efroimskymethod in its present form is not compatible with the Isaacson limit ofhigh-frequency gravitational waves, and we propose its natural generalizationto resolve this drawback.Comment: 7 pages, to appear in Class. Quantum Gra

The Efroimsky formalism for weak gravitational waves adapted to high-frequency perturbations