Radiation reaction in curved space-time: local method

TL;DR

This paper introduces a local method for deriving radiation reaction forces in curved space-time, avoiding previous ambiguities by using field quantities defined solely on the particle's world-line, and extends results to non-vacuum backgrounds.

Contribution

A new local derivation of radiation reaction in curved space-time that resolves previous ambiguities and applies to scalar, electromagnetic, and gravitational fields, including non-vacuum backgrounds.

Findings

Scalar and vector divergences cancel for specific charge ratios.

The local method successfully derives radiation reaction forces.

Progress made in extending results to non-vacuum space-times.

Abstract

Although consensus seems to exist about the validity of equations accounting for radiation reaction in curved space-time, their previous derivations were criticized recently as not fully satisfactory: some ambiguities were noticed in the procedure of integration of the field momentum over the tube surrounding the world-line. To avoid these problems we suggest a purely local derivation dealing with the field quantities defined only {\em on the world-line}. We consider point particle interacting with scalar, vector (electromagnetic) and linearized gravitational fields in the (generally non-vacuum) curved space-time. To properly renormalize the self-action in the gravitational case, we use a manifestly reparameterization-invariant formulation of the theory. Scalar and vector divergences are shown to cancel for a certain ratio of the corresponding charges. We also report on a modest progress in extending the results for the gravitational radiation reaction to the case of non-vacuum background.