Radiation reaction and energy-momentum conservation

Abstract

We discuss subtle points of the momentum balance for radiating particles in flat and curved space-times. An instantaneous balance is obscured by the presence of the Schott term which is a finite part of the bound field momentum. To establish the balance, one has to take into account the initial and final conditions for acceleration, or to apply averaging. In curved space-time, an additional contribution arises from the tidal deformation of the bound field. This force is shown to be the finite remnant from the mass renormalization and it is different both from the radiation recoil force and the Schott force. For radiation of nongravitational nature from point particles in curved space-time the reaction force can be computed by substituting the retarded field directly to the equations of motion. A similar procedure is applicable to gravitational radiation in a vacuum space-time, but fails in the non-vacuum case. The existence of the gravitational quasilocal reaction force in this general case seems implausible, though it still exists in the nonrelativistic approximation. We also explain the putative antidamping effect for gravitational radiation under non-geodesic motion and derive the nonrelativistic gravitational quadrupole Schott term. Radiation reaction in curved space of dimension other than four is also discussed. © 2011 Springer Science+Business Media B.V.