Main Question or Discussion Point
Is it accurate in any sense of the word to think of electromagnetic radiation, ala chapter 7-8 of Landau, and gravitational radiation, ala https://n.ethz.ch/~usoler/download/GR/Spacetime%20and%20Geometry.pdf [Broken], as the classical field theoretical analogue of inelastic (& elastic?) scattering, the way you could loosely think of electromagnetic waves (free field solutions of Maxwell) as the field theoretical analogue of the harmonic oscillator of particle Lagrangian mechanics? Is it too much of a stretch to call gravitational waves an analogue of the Harmonic oscillator as well?
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