Self-force via a Green’s function decomposition

Abstract

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