Are Time-Domain Self-Force Calculations Contaminated by Jost Solutions?

TL;DR

This paper investigates the potential contamination of time-domain self-force calculations by Jost junk solutions, identifying the source of the issue and proposing correct source implementation as a solution.

Contribution

It clarifies the origin of Jost solutions in self-force calculations and establishes proper source implementation as a key to avoiding contamination.

Findings

Jost solutions are caused by incorrect translation of singular sources into jump conditions.

Proper late-time source implementation prevents Jost junk solutions.

The study improves the reliability of time-domain self-force computations.

Abstract

The calculation of the self force in the modeling of the gravitational-wave emission from extreme-mass-ratio binaries is a challenging task. Here we address the question of the possible emergence of a persistent spurious solution in time-domain schemes, referred to as a {\em Jost junk solution} in the literature, that may contaminate self force calculations. Previous studies suggested that Jost solutions are due to the use of zero initial data, which is inconsistent with the singular sources associated with the small object, described as a point mass. However, in this work we show that the specific origin is an inconsistency in the translation of the singular sources into jump conditions. More importantly, we identify the correct implementation of the sources at late times as the sufficient condition guaranteeing the absence of Jost junk solutions.