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.

“Flux-balance formulae” for extreme mass-ratio inspirals

“…We expect that a most advanced self-force code (such as the one of Ref. [64]) will soon be able to test this relation directly.…”

“…Furthermore, the flux formulae are a (quasi-)gauge-invariant characterization of the radiative dynamics for such generic orbits. Therefore, we expect that concrete calculation of the flux formulae will clarify the interesting possibility of "sustained" resonance in extreme mass-ratio inspirals (the orbit "stuck" on the resonance) [45,61], help in refining known practical schemes for simulating radiative extreme-mass-ratio inspirals [6,25,[62][63][64], and provide (yet another) accurate strong-field benchmark for the extreme mass-ratio regime of a more generic two-body problem in general relativity (see, e.g., Ref. [65]).…”

“…this is the so-called "forcing term" in Refs. [16,61,62,64]. The objective of this appendix is to examine how this expression can be derived in the Hamiltonian formulation.…”

Quasicircular inspirals and plunges from nonspinning effective-one-body Hamiltonians with gravitational self-force information

“…The results, corroborated by the use of several gauges and numerical techniques (see, e.g., Ref. [10] and references therein), have been already used to evolve extreme-mass-ratio-inspirals (EMRIs) around a Schwarzschild black-hole [60,61] and they represent a key input for EMRI waveform modeling schemes recently developed [62] and under development [63].…”

Scalar self-force for high spin black holes

“…Notably, second order results are required to reach the desired accuracy for LISA and increasing the efficiency of computations will be indispensable to attain reasonable coverage of the large parameter space. Steps have been taken to address these issues [11,12] but further significant efforts will be required to be able to fully exploit the science potential of EMRIs with LISA.…”