I've been exploring the concept of gravitational wave (G-wave) emission from symmetrically accelerating systems and have encountered a puzzling question. Standard sources typically state that symmetrical systems, such as a perfectly rotating sphere, do not emit G waves. As they require a changing quadrupole moment, which such systems do not exhibit. However, this leads me to draw parallels with concepts like standing waves and the Fourier transform of a static field, where individual waves can cancel each other out, resulting in what appears to be a static field.
My question, therefore: Is it that each part of a symmetrically accelerating system never actually emits any gravitational waves, or is it more accurate to say that any potential gravitational waves are effectively cancelled out due to the system's symmetry?
To illustrate this, consider a hypothetical scenario: If a rotating spherical mass were to suddenly appear in an ideal space-time, would an observer detect non-zero gravitational waves during the initial moments when the gravitational effects from different parts of the sphere begin to propagate at the speed of light (c)?
