Time-domain metric reconstruction for hyperbolic scattering

TL;DR

This paper develops a novel time-domain method for self-force calculations on scatter orbits in Schwarzschild spacetime, enabling more accurate modeling of hyperbolic encounters in general relativity.

Contribution

It introduces a new technique using jump conditions for Hertz potential reconstruction applicable to scatter orbits, extending existing methods beyond bound orbits.

Findings

Derived closed-form jump conditions for Hertz potential

Implemented a numerical scheme for scatter orbits in Schwarzschild spacetime

Paved the way for future self-force and orbital dynamics calculations

Abstract

Self-force methods can be applied in calculations of the scatter angle in two-body hyperbolic encounters, working order by order in the mass ratio (assumed small) but with no recourse to a weak-field approximation. This, in turn, can inform ongoing efforts to construct an accurate model of the general-relativistic binary dynamics via an effective-one-body description and other semi-analytical approaches. Existing self-force methods are to a large extent specialised to bound, inspiral orbits. Here we develop a technique for (numerical) self-force calculations that can efficiently tackle scatter orbits. The method is based on a time-domain reconstruction of the metric perturbation from a scalar-like Hertz potential that satisfies the Teukolsky equation, an idea pursued so far only for bound orbits. The crucial ingredient in this formulation are certain jump conditions that (each multipole mode of) the Hertz potential must satisfy along the orbit, in a 1+1-dimensional multipole reduction of the problem. We obtain a closed-form expression for these jumps, for an arbitrary geodesic orbit in Schwarzschild spacetime, and present a full numerical implementation for a scatter orbit. In this paper we focus on method development, and go only as far as calculating the Hertz potential; a calculation of the self-force and its physical effects on the scatter orbit will be the subject of forthcoming work.