# Do dipolar gravitational waves exist?

There seems to be some controversy (see A, B) on this topic, so I'm posting a new question for discussion and clarification.

By definition, one cannot accelerate the center of mass of a closed system (to do so would require a force from outside the system). So, seen from afar, gravitational waves radiating from a closed system can come only from an accelerating redistribution of mass within the system (quadrupolar effect). (BTW radiating waves are defined as having a 1/r dependence on distance, rather than 1/r2 for local static gravitational fields).

At intermediate distances (large compared to some component of the system but small compared to the whole system), the situation is less clear. For example, in a binary orbiting system with two compact masses, you could be at a large distance from one mass compared with its diameter but at a small distance compared to the separation of the two masses. So, the question arises: is there a regime where gravitational effects decay closely as 1/r with distance from an individual mass? An individual mass does not represent a closed system and is not bound by quadrupole effect, so this radiation could be viewed as radiating from a dipolar source.
Several authors explore the idea that quadrupole radiation can be derived as the residue left from partial cancellation of radiating dipole fields [C, D]. The dipole fields from different sources within the closed system do not cancel completely because the sources are not exactly colocated. Some of these analyses invoke the gravitoelectromagnetic approximation as an analogy with electromagnetics.

To some extent this is semantics about what constitutes a radiating field - or perhaps separating the sources is just a mathematical contrivance. But it seems like an answer could be gauged by looking at numerical simulations to see if there is indeed a $$1/r$$ regime not too far from one or the other of the two masses but still nearby or inside the total system.