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 multiple
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.