Time-asymmetric structure of gravitational radiation

Gravitational radiation reaction effects in the dynamics of an isolated system arise from the use of retarded potentials for the radiation field, satisfying time-asymmetric boundary conditions imposed at past-null infinity. Part one of this paper investigates the ‘‘antisymmetric’’ component, a solution of the wave equation of the type retarded minus advanced, of the linearized gravitational field generated by an isolated system in the exterior region of the system. At linearized order such a component is well defined and is ‘‘time odd’’ in the usual post-Newtonian (PN) sense. We introduce a new linearized coordinate system which generalizes the Burke and Thorne coordinate system both in its space-time domain of validity, which is no longer limited to the near zone of the source, and in the post-Newtonian smallness of the linear antisymmetric (‘‘time-odd’’) component of the metric, for all multipolarities of antisymmetric waves. These waves (as viewed in the near zone) define a generalized radiation reaction four-tensor potential ${\mathit{V}}_{\mathrm{react}}^{\mathrm{\alpha }\mathrm{\beta }}$ of the linear theory.