Self-force via a Green’s function decomposition

The gravitational field in a neighborhood of a particle of small mass μ moving through curved spacetime is naturally decomposed into two parts each of which satisfies the perturbed Einstein equations through O(μ). One part is an inhomogeneous field which looks like the μ/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(μ) 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(μ). In the light of all previous work this is quite an unexpected result.