of gravitational waves would help scientists to sort out what to look for from a
seemingly huge mess of observational data.
As an example of the possible sources of gravitational waves for LISA detec-
tion [1], a binary inspiral of a small black hole of solar mass and a supermassive
black hole of 105 to 107 solar mass, what we call an extreme mass-ratio system, can
be taken. Such black holes are now believed to reside in the cores of many galaxies,
including our own.
Designing the theoretical waveform from this binary system would require an
accurate description of the orbital evolution of the small black hole. The orbital
motion can be modeled by considering a pointlike test particle moving in the
gravitational field which results from combining the field of the large black hole
with the much smaller field of the small black hole using perturbation techniques.
The resulting motion then includes the effects of radiation reaction and the self-
force.
This dissertation presents specific methods for calculating the effects of
radiation reaction and the self-force for the extreme mass-ratio systems. We explore
two models of such systems in the main body of the dissertation. The case of a
scalar particle orbiting a Schwarzschild black hole is investigated first, and the
case of a point mass orbiting a Schwarzschild black hole follows. The study of the
former itself might not provide physical interpretations as directly applicable to our
gravitational wave physics, but it provides valuable computational tools with which
we can approach the latter. The entire dissertation can be outlined as follows.
In ('!i lpter 2 we introduce general formal schemes on radiation reaction.
Two main articles on this subject by Dirac [2] and by Dewitt and Brehme [3] are
reviewed.
In ('! Ilpter 3 we revisit the general formal schemes and review briefly the
structure of the equations of motion for the self-force for each case from Dirac to