From the self-force problem to the Radiation reaction formula

TL;DR

This paper reviews recent theoretical advances in the self-force problem in general relativity, emphasizing the importance of gauge-invariant motion concepts for gravitational wave detection.

Contribution

It introduces a new perspective on defining gauge-invariant notions of motion within the self-force problem using black hole perturbation theory.

Findings

Progress in formulating gauge-invariant descriptions of motion

Clarification of the self-force problem's conceptual foundations

Implications for gravitational wave observations

Abstract

We review a recent theoretical progress in the so-called self-force problem of a general relativistic two-body system. Although a two-body system in Newtonian gravity is a very simple problem, some fundamental issues are involved in relativistic gravity. Besides, because of recent projects for gravitational wave detection, it comes to be possible to see those phenomena directly via gravitational waves, and the self-force problem becomes one of urgent and highly-motivated problems in general relativity. Roughly speaking, there are two approaches to investigate this problem; the so-called post-Newtonian approximation, and a black hole perturbation. In this paper, we review a theoretical progress in the self-force problem using a black hole perturbation. Although the self-force problem seems to be just a problem to calculate a self-force, we discuss that the real problem is to define a gauge invariant concept of a motion in a gauge dependent metric perturbation.