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.Comment: a special issue for Classical and Quantum Gravity, a review article
of Capra Ranch Meeting
