Frequency-domain approach to self-force in hyperbolic scattering

The self-force problem in gravity is an approach to the two-body problem in which the mass ratio is extreme enough that the smaller-mass body can be usefully treated as a test particle to the lowest order in the mass ratio. In this paper, frequency domain methods, which are particularly suited for bound orbital motion, are developed in an innovative way so that they can be applied to study hyperbolic scattering in the ``toy'' problem of a scalar charge. Frequency domain methods as developed here may prove to be a promising approach to the full gravitational self-force problem.