Frequency-domain approach to self-force in hyperbolic scattering

Understand

We develop a frequency-domain method for calculating the self-force acting on a scalar charge on a fixed scattering geodesic in Schwarzschild spacetime.

• Existing frequency-domain methods, which are tailored for bound orbits, are inadequate here for several reasons.
• One must account for the continuous spectrum in the scattering problem, deal with slowly-convergent radial integrals that are hard to evaluate numerically, and confront the inapplicability of the standard self-force method of "extended homogeneous solutions", which only works for compactly supported sources.
• We tackle each of these issues in turn, and then present a full numerical implementation, in which we calculate the self-force correction to the scatter angle due to scalar-field back-reaction.