Not inverse square law, but simply inverse law. As energy radiates outwards, it becomes diluted on a sphere that increases its surface area as r^2. Thus the lo

Not inverse square law, but simply inverse law. As energy radiates outwards, it becomes diluted on a sphere that increases its surface area as r^2. Thus the local energy density goes with inverse square law in the distance to the observer. But we don't measure the local energy density of gravitational waves, but the local amplitude. And in wave mechanics energy is the square of the amplitude. So the amplitude goes down with 1/r.