Self-force via a Green's function decomposition

TL;DR

This paper presents a decomposition of a particle's gravitational field into inhomogeneous and homogeneous parts, enabling precise calculation of self-force effects, including radiation reaction, in curved spacetime.

Contribution

It introduces a Green's function decomposition method to analyze self-force effects for scalar, electromagnetic, and gravitational fields in curved spacetime.

Findings

Decomposition separates field into parts satisfying perturbed Einstein equations.

Homogeneous part includes tail term crucial for self-force calculation.

Method applies uniformly across different field types.

Abstract

The gravitational field of a particle of small mass \mu moving through curved spacetime is naturally decomposed into two parts each of which satisfies the perturbed Einstein equations through O(\mu). One part is an inhomogeneous field which, near the particle, looks like the \mu/r field distorted by the local Riemann tensor; it does not depend on the behavior of the source in either the infinite past or future. The other part is a homogeneous field and includes the ``tail term''; it completely determines the self force effects of the particle interacting with its own gravitational field, including radiation reaction. Self force effects for scalar, electromagnetic and gravitational fields are all described in this manner.