Mino, Sasaki, and Tanaka, and Quinn and Wald [2, 3, 4, 5, 6]. Then, we provide
two examples of the purely analytic attempts to the self-force calculations by
Dewitt and Dewitt [7] and Pfenning and Poisson [8].
In ('!i lpter 4 we introduce a hybrid of both analytical and numerical methods,
known as the "mode-- iin method devised by Barack and Ori [9], in order to
handle more general problems than the purely analytical approaches can. We
then work on the case of a scalar particle orbiting a Schwarzschild black hole via
this method. The self-force calculations for this case involve analytical work for
determining R.i /J ;,.,, .: ,/.:.n Parameters, which refer to the mode-decomposed
multiple moments of the singular part of the scalar field. The computations of the
regularization parameters are facilitated via a local analysis of spacetime, and an
elaborate perturbation analysis of the local geometry is developed for this purpose.
The regularization parameters are calculated to sufficiently high orders so that
their use in the mode sums for the self-force calculation will result in more rapid
convergence and more accurate final results. These analytical results are then
combined with the numerical computations of the retarded field to provide the
self-force ultimately.
In C'!i lpter 5 we provide a method to determine the effects of the gravitational
self-force on a point mass orbiting a Schwarzschild black hole. First, we address the
gauge issues in relation to MiSaTaQuWa Gravitational Self-force [4, 5]. Then we
follow a recent analysis by Detweiler [10] to describe the gravitational field, which
is the perturbation created by the point mass from the background spacetime. To
avoid the gauge problem, rather than calculating the self-force directly, we focus
on gauge invariant quantities and determine their changes due to the self-force
effects. Techniques involved in calculating the regularization parameters for the
gravitational field case are more complicated than for the scalar field case. We