Fast Self-forced Inspirals

TL;DR

This paper introduces a rapid and efficient method for modeling extreme mass-ratio inspirals and their gravitational waves, significantly reducing computation time while maintaining high accuracy by incorporating self-force effects.

Contribution

The authors develop a novel averaging-based approach that speeds up inspiral trajectory calculations by 2-5 orders of magnitude and accurately incorporates self-force effects.

Findings

Trajectory computation in milliseconds, a 2-5 order speedup.

Waveform mismatch less than 10^{-4} over two years.

Method easily integrates with existing self-force results.

Abstract

We present a new, fast method for computing the inspiral trajectory and gravitational waves from extreme mass-ratio inspirals that can incorporate all known (and future) self-force results. Using near-identity (averaging) transformations we formulate equations of motion that do not explicitly depend upon the orbital phases of the inspiral, making them fast to evaluate, and whose solutions track the evolving constants of motion, orbital phases and waveform phase of a full self-force inspiral to $O(\eta)$, where $\eta$ is the (small) mass ratio. As a concrete example, we implement these equations for inspirals of non-spinning (Schwarzschild) binaries. Our code computes inspiral trajectories in milliseconds which is a speed up of 2-5 orders of magnitude (depending on the mass-ratio) over previous self-force inspiral models which take minutes to hours to evaluate. Computing two-year duration waveforms using our new model we find a mismatch better than $\sim 10^{-4}$ with respect to waveforms computed using the (slower) full self-force models. The speed of our new approach is comparable with kludge models but has the added benefit of easily incorporating self-force results which will, once known, allow the waveform phase to be tracked to sub-radian accuracy over an inspiral.