This is fascinating, thank you! You’re absolutely correct, the single GR course i took linearized the EFE for the section on gravity waves and the concept that

This is fascinating, thank you! You’re absolutely correct, the single GR course i took linearized the EFE for the section on gravity waves and the concept that gravitation self-gravitates did not really come through. In hindsight maybe that should have been obvious though, since all waves have this property.