I must admit that my curiosity is piqued by this.
Ok, one takes a magnet, and shakes it back and forth. The acceleration of the magnetic field produces a wave.
Take a star and shake it back and forth, gravitational waves result, as the gravitational attraction that that star exerts on another object would vary sinosodaly. It does seem like gravitational waves, or at least the appearance of them can be predicted by Newtonian mechanics. Could somebody show me the flaw in this?