Comparing second-order gravitational self-force, numerical relativity, and effective one body waveforms from inspiralling, quasicircular, and nonspinning black hole binaries

Abstract

We present the first systematic comparison between gravitational waveforms emitted by inspiralling, quasi-circular and nonspinning black hole binaries computed with three different approaches: second-order gravitational self-force (2GSF) theory, as implemented in the 1PAT1 model; numerical relativity (NR), as implemented by the SXS collaboration; and the effective one body (EOB) formalism, as implemented in the TEOBResumS waveform model. To compare the models we use both a standard, time-domain waveform alignment and a gauge-invariant analysis based on the dimensionless function Qω(ω) ≡ ω 2 / ω, where ω is the gravitational wave frequency. We analyse the domain of validity of the 1PAT1 model, deriving error estimates and showing that the effects of the final transition to plunge, which the model neglects, extend over a significantly larger frequency interval than one might expect. Restricting to the inspiral regime, we find that, while for mass ratios q = m1/m2 ≤ 10 TEOBResumS is largely indistinguishable from NR, 1PAT1 has a significant dephasing ≳ 1 rad; conversely, for q ≳ 100, 1PAT1 is estimated to have phase errors < 0.1 rad on a large frequency interval, while TEOBResumS develops phase differences ≳ 1 rad with it. Most crucially, on that same large frequency interval we find good agreement between TEOBResumS and 1PAT1 in the intermediate regime 15 ≲ q ≲ 64, with < 0.5 rad dephasing between them. A simple modification to the TEOBResumS flux further improves this agreement for q ≳ 30, reducing the dephasing to ≈ 0.27 rad even at q = 128. While our analysis points to the need for more highly accurate, long-inspiral, NR simulations for q ≳ 15 to precisely quantify the accuracy of EOB/2GSF waveforms, we can clearly identify the primary sources of error and routes to improvement of each model. In particular, our results pave the way for the construction of GSF-informed EOB models for both intermediate and extreme mass ratio inspirals for the next generation of gravitational wave detectors.

Resonant dynamics of extreme mass-ratio inspirals in a perturbed Kerr spacetime

“…By combining the results in these studies, one should be able to build an EMRI waveform model (on top of the EMRI waveform model on a Kerr background) for a generic Kerr perturbation h. This method is not only important for future space-borne gravitational-wave detection, but likely also useful for constructing waveforms to test modified gravity theories using comparable mass-ratio binaries in the band of ground-based gravitational-wave detectors. Indeed, for waveforms consistent with general relativity, there is literature [67][68][69][70][71][72][73][74][75][76] pointing out that the EMRI-inspired waveform, with an appropriate rescaling using the massratio parameter, agrees surprisingly well with the waveform obtained from numerical relativity for comparable massratio systems. As the EMRI method does not require the post-Newtonian or post-Minkowskian expansion, it will serve as a promising route for generating high-precision waveforms for comparable mass-ratio binaries.…”

Metric perturbations of Kerr spacetime in Lorenz gauge: circular equatorial orbits

“…Second, the asymptotic behaviour of the Lorenz gauge MP towards the horizon and infinity is well-understood. Third, the existing Lorenz-gauge set-up has been successfully used in the Schwarzschild case for second-order calculations [21,[59][60][61][62][63]. Fourth, the Lorenz-gauge MP has been computed by other means (e.g.…”

Spinning test body orbiting around a Kerr black hole: Comparing spin supplementary conditions for circular equatorial orbits

“…This fact is especially pronounced in the modelling of extreme mass ratio inspirals [16][17][18][19][20][21][22], in which a stellar compact object, like a black hole or a neutron star, inspirals in the background of a supermassive black hole. Even when calibrating the GW waveforms, the starting points are CEOs [23,24]. Hence, in our study we focus on CEOs of an extended test body in pole-dipole-(spin induced) quadrupole approximation around a Kerr black hole.…”