Derivation of Gravitational Self-Force

TL;DR

This paper rigorously derives the gravitational self-force in general relativity by analyzing the motion of scaled-down bodies, establishing that their limiting trajectories are geodesics with perturbative corrections including self-force and spin effects.

Contribution

It provides a rigorous derivation of the gravitational self-force and related effects using a systematic perturbative approach, clarifying the status of the MiSaTaQuWa equation.

Findings

Limiting worldline is a geodesic of the background metric.

Leading order corrections include self-force, spin force, and geodesic deviation.

The MiSaTaQuWa equation is identified as a candidate self-consistent perturbative equation.

Abstract

We analyze the issue of ``particle motion'' in general relativity in a systematic and rigorous way by considering a one-parameter family of metrics corresponding to having a body (or black hole) that is ``scaled down'' to zero size and mass in an appropriate manner. We prove that the limiting worldline of such a one-parameter family must be a geodesic of the background metric and obtain the leading order perturbative corrections, which include gravitational self-force, spin force, and geodesic deviation effects. The status the MiSaTaQuWa equation is explained as a candidate ``self-consistent perturbative equation'' associated with our rigorous perturbative result