Radiation reaction and energy-momentum conservation

TL;DR

This paper analyzes the complex momentum balance for radiating particles in flat and curved space-time, highlighting the roles of the Schott term, initial conditions, and tidal effects, and discusses implications for gravitational radiation reaction.

Contribution

It clarifies the momentum balance including the Schott term and tidal effects, and explores the computation of reaction forces in curved space-time, extending understanding of radiation reaction beyond flat space.

Findings

The Schott term affects instantaneous momentum balance.

Tidal deformation contributes to reaction forces in curved space.

Gravitational reaction force can be computed via retarded fields in vacuum.

Abstract

We discuss subtle points of the momentum balance for radiating particles in flat and curved space-time. 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 form the radiation recoil force and the Schott force. For radiation of non-gravitational nature from point particles in curved space-time the reaction force can be computed substituting the retarded field directly to the equations of motion. Similar procedure is applicable to gravitational radiation in 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 non-relativistic approximation. We also explain the putative antidamping effect for gravitational radiation under non-geodesic motion and derive the non-relativistic gravitational quadrupole Schott term. Radiation reaction in curved space of dimension other than four is also discussed