Binary systems radiate energy away in gravitational waves as the orbits of the two masses spiral in towards each other. My understanding of gravity is that we think of it as a mediator of particle-particle interactions. If we expect there to be a massless force carrying boson for gravity, then we expect gravity mediates interactions between masses. However, if one considers a binary system assuming no other masses in the system, general relativity still predicts gravitational waves.
In comparison electrodynamics has a similar case when modeling a particle in the presence of the purely retarded field of another particle. One must include the radiation reaction self-force in order to get the correct equations of motion as we observe. However Wheeler-Feynman electrodynamics allow us to think of this model not as a general model for two interacting particles but a model in which two particles interact in the presence of fixed charges (absorbers) stationed an infinite distance away in all directions. In this way the field only mediates interactions between charges, the "field" itself cannot carry energy off to infinity if there are no charges at infinity.
I realize Wheeler-Feynman still has some issues when quantization as there is no mass normalization which is required for the lamb shift. I've read there are corrections/tricks to make it work though. I'm not concerned with quantization as much as I am with a classical picture in which an interaction is mediated by a field or in this case a metric. It seems problematic that gravity can carry radiation off to infinity with no matter capable of absorbing it at infinity. The traditional approach to Maxwell's laws is equivalent to the stipulation in Wheeler-Feynman electrodynamics that all "free" radiation is absorbed by matter not explicitly included in the model. It seems to me gravity should have such a formulation if we believe it to mediate interactions between particles. I realize that relativity implies a mass energy equivalence and the solution might be that spacetime itself can contain the energy with no contradiction. I would like to see an argument for this if this is indeed the case.
Since gravity doesn't have a superposition principle like E&M, I don't get how one would construct such a theory. Does this mean a Wheeler-Feynman formulation of gravity is not possible?