Self-force via a Green's function decomposition

The gravitational field in a neighborhood of a particle of small mass mu moving through curved spacetime is naturally decomposed into two parts each of which satisfies the perturbed Einstein equations through O(mu). One part is an inhomogeneous field which looks like the mu/r field tidally distorted by the local Riemann tensor. The other part is a homogeneous field that completely determines the self-force of the particle interacting with its own gravitational field, which changes the worldline at O(mu) and includes the effects of radiation reaction. Surprisingly, a local observer measuring the gravitational field in a neighborhood of a freely moving particle sees geodesic motion of the particle in a perturbed vacuum geometry and would be unaware of the existence of radiation at O(mu). In the light of all previous work this is quite an unexpected result.