Fast self-forced inspirals

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 with errors of at most order , where η is the small mass ratio. As a concrete example, we implement these equations for inspirals of non-spinning binaries. Our code computes inspiral trajectories in milliseconds which, depending on the mass-ratio, is a speed up of 2–5 orders of magnitude 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 smaller than ∼10−4 with respect to waveforms computed using 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.