The Efroimsky formalism adapted to high-frequency perturbations

TL;DR

This paper reviews the Efroimsky perturbation scheme for gravitational waves, compares it with Isaacson's approach, identifies a compatibility issue at high frequencies, and proposes a generalization to address this problem.

Contribution

It introduces a generalized Efroimsky formalism that overcomes the incompatibility with Isaacson's high-frequency limit.

Findings

Efroimsky scheme is not compatible with Isaacson's high-frequency limit

A natural generalization of Efroimsky formalism is proposed

The generalized method aligns with Isaacson's approach at high frequencies

Abstract

The Efroimsky perturbation scheme for consistent treatment of gravitational waves and their influence on the background is summarized and compared with classical Isaacson's high-frequency approach. We demonstrate that the Efroimsky method in its present form is not compatible with the Isaacson limit of high-frequency gravitational waves, and we propose its natural generalization to resolve this drawback.