CHAPTER 6
CONCLUSION
A binary inspiral of a small black hole of solar mass and a supermassive black
hole of 105 to 107 solar mass, called an extreme mass-ratio system, is one of the
possible target sources of gravitational waves for LISA detection [1]. An accurate
description of the orbital motion of the small black hole, including the effects
of radiation reaction and the self-force is essential to designing the theoretical
waveform from this binary system.
In this dissertation we have presented specific methods for calculating the
effects of radiation reaction and the self-force for the two models of such systems:
the case of a scalar particle orbiting a Schwarzschild black hole and the case of a
point mass orbiting a Schwarzschild black hole. In both cases our calculations have
been implemented via the "mode--, iin method pioneered by Barack and Ori [9],
in which the self-force or the effects of self-force are evaluated from the difference
between the particle's own field and its singular part via mode-decomposed
multiple moments of each as in Eq. (4-32) or Eqs. (5-38) and (5-39).
The mode-decomposed multiple moments of the singular field are described
by R. gul'. .:.Il...': ', Parameters as represented in Eqs. (4-33)-(4-44) for the case of
the scalar field and in Eqs. (5-73)-(5-79), (5-112)-(5-122) and (5-164)-(5-171) for
the case of gravitational field. The determination of regularization parameters has
involved the two main analytical tasks: a local analysis of spacetime geometry
and structure analyses of the singular field. The local analysis of spacetime
geometry has provided powerful tools, such as THZ normal coordinates as shown
in Eqs. (4-129)-(4-141) along with Eqs. (4-117) and (4-118). With these we have
obtained the simplest expression for the singular field as in Eq. (4-45) for the