That depends on what gauge you're working in. What you say is true for the TT gauge, but not for other choices of gauge. See, e.g., section 1.3 of Maggiore's Gravitational Waves book.
That depends on what gauge you're working in. What you say is true for the TT gauge, but not for other choices of gauge. See, e.g., section 1.3 of Maggiore's Gravitational Waves book.