I have just learned that linear frame dragging exists in General Relativity. I have also seen simulations where a periodically accelerated and decelerated mass causes a sort of gravitational dipole radiation, dragging nearby masses in the direction of the acceleration. My problem with this is that in my whole life I was taught that the leading order in gravitational radiation is quadrupole; dipole radiation can't exist because of conservation of linear and angular momentum. Is dipole radiation forbidden only in linearized General Relativity? What is the full picture here / what am I missing?
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