Radiation reaction in curved spacetime

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 (Laser Interferometer Space Antenna) detection. 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.; One can calculate 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. As for the former, the interaction of a scalar point charge with its own field results in the self-force on the particle, which includes but is more general than the radiation reaction force. In the vicinity of the particle in curved spacetime, one may follow Dirac and split the retarded field of the particle into two parts: (1) the singular source field which resembles the Coulomb potential near the particle, and (2) the regular remainder field. The singular source field exerts no force on the particle, and the self-force is entirely caused by the regular remainder. As for the latter, a point mass interacts with the metric perturbations created by itself when it moves through the background geometry. Similarly, the perturbation field can be split into two parts: (1) the singular source field which resembles the Coulomb potential near the particle, tidally distorted by the local Riemann tensor of the background and exerts no force back on the particle itself, and (2) the regular remainder field which is entirely responsible for the self-force as the particle moves along a geodesic of the perturbed geometry.; In this dissertation we describe systematic methods for finding multipole decompositions of the singular source fields for both cases. This important step leads to the calculation of the self-force on a scalar-charged particle or a point mass orbiting a Schwarzschild black hole.