Gravitational Radiation Reaction to a Particle Motion

TL;DR

This paper derives the leading order correction to a particle's motion due to gravitational radiation reaction, using two different methods, and discusses the implications of the resulting equation of motion.

Contribution

It introduces a novel derivation of the gravitational radiation reaction correction to particle motion, extending methods from electromagnetic theory to gravity.

Findings

Derived the equation of motion using two different approaches.

Found the same equation of motion from both methods.

Discussed the implications of the gravitational radiation reaction correction.

Abstract

In this paper, we discuss the leading order correction to the equation of motion of the particle, which presumably describes the effect of gravitational radiation reaction. We derive the equation of motion in two different ways. The first one is an extension of the well-known formalism by DeWitt and Brehme developed for deriving the equation of motion of an electrically charged particle. In contrast to the electromagnetic case, in which there are two different charges, i.e., the electric charge and the mass, the gravitational counterpart has only one charge. This fact prevents us from using the same renormalization scheme that was used in the electromagnetic case. To make clear the subtlety in the first approach, we then consider the asymptotic matching of two different schemes, i.e., the internal scheme in which the small particle is represented by a spherically symmetric black hole with tidal perturbations and the external scheme in which the metric is given by small perturbations on the given background geometry. The equation of motion is obtained from the consistency condition of the matching. We find that in both ways the same equation of motion is obtained. The resulting equation of motion is analogous to that derived in the electromagnetic case. We discuss implications of this equation of motion.