Are time-domain self-force calculations contaminated by Jost solutions?

Institut de Ciencies de l’Espai (CSIC-IEEC), Facultat de Ciencies, Campus UAB, Torre C5 parells, 08193 Bellaterra, Spain(Dated: January 13, 2011)The modeling of the gravitational-wave emission from extreme-mass-ratio inspirals is crucial fortheir detection and analysis with the future space-based observatory LISA. The inspiral can bedescribed as the action of a local force, the self-force, determined by the gravitational perturbationscreated by the small object, described as a point mass, on the background geometry. The calculationof the self-force is a challenging task that requires the control of sources of error such as spuriousmodes or numerical noise. Here we address the question of the possible emergence of a persistentspurious solution in time-domain schemes, referred to as a Jost junk solution in the literature, thatmay contaminate self-force calculations. Previous studies suggested that Jost solutions are due tothe use of zero initial data, which is inconsistent with the singular sources associated with the pointmass. However, in this work we show that the speci c origin is an inconsistency in the translation ofthe singular sources into jump conditions. More importantly, we identify the correct implementationof the sources at late times as the sucient condition guaranteeing the absence of Jost junk solutions.