The gravitational self-force

TL;DR

This paper reviews the theoretical foundations of the gravitational self-force, explaining how a small body's motion in curved spacetime is affected by its own gravitational field, with implications for gravitational wave detection.

Contribution

It provides a comprehensive review of the self-force theory, including methods to compute the effect for small bodies near massive black holes, advancing gravitational wave source modeling.

Findings

Decomposition of the retarded field into singular and smooth parts.

Matched asymptotic expansions for small black hole motion.

Progress in computing self-force effects for extreme mass ratio systems.

Abstract

The self-force describes the effect of a particle's own gravitational field on its motion. While the motion is geodesic in the test-mass limit, it is accelerated to first order in the particle's mass. In this contribution I review the foundations of the self-force, and show how the motion of a small black hole can be determined by matched asymptotic expansions of a perturbed metric. I next consider the case of a point mass, and show that while the retarded field is singular on the world line, it can be unambiguously decomposed into a singular piece that exerts no force, and a smooth remainder that is responsible for the acceleration. I also describe the recent efforts, by a number of workers, to compute the self-force in the case of a small body moving in the field of a much more massive black hole. The motivation for this work is provided in part by the Laser Interferometer Space Antenna, which will be sensitive to low-frequency gravitational waves. Among the sources for this detector is the motion of small compact objects around massive (galactic) black holes. To calculate the waves emitted by such systems requires a detailed understanding of the motion, beyond the test-mass approximation.