Shifted geodesic scheme for computing asymptotic GW fluxes from a spinning body

Characterizing the motion of spinning bodies near black holes is crucial for enhancing gravitational-wave models for the LISA science program. Moreover, this analysis illuminates a limit of the general relativistic two-body problem that can be computed precisely, serving as a benchmark for calculations across mass ratios. Recently, several methods for accurately modeling completely generic orbits of spinning bodies in large mass ratio systems have been introduced. These include the pioneering Hamilton-Jaocbi formulation by Witzany, 2019 (arxiv.org/abs/1903.03651), as well as the frequency-domain approach of Drummond & Hughes, 2022a,b (arxiv.org/abs/2201.13334, arxiv.org/abs/2201.13335). Gravitational-wave energy and angular momentum asymptotic fluxes from a spinning body have been computed in the Teukolsky formalism up to linear-order in secondary spin by Skoupý et al., 2023 (arxiv.org/abs/2303.16798), using the Drummond & Hughes description of the spinning body's motion. The speed of computation of the fluxes presented in this analysis is limited by the time taken to calculate the spinning-body trajectory. In this talk, I will present preliminary results for a “shifted geodesic” approximation scheme which aims to speed up the evaluation of these fluxes. Here, we approximate the spinning-body trajectory as a geodesic with its associated frequencies shifted such that they correspond to the those of a spinning body. In this way, we can expedite our calculation by leveraging existing infrastructure for computing adiabatic gravitational-wave fluxes along geodesic orbits using the Teukolsky formalism. In particular, we extend the framework of the GREMLIN package, which is a frequency-domain Teukolsky solver written in C++ and developed by Scott Hughes.