197 research outputs found

    Black hole perturbation theory and gravitational self-force

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    Much of the success of gravitational-wave astronomy rests on perturbation theory. Historically, perturbative analysis of gravitational-wave sources has largely focused on post-Newtonian theory. However, strong-field perturbation theory is essential in many cases such as the quasinormal ringdown following the merger of a binary system, tidally perturbed compact objects, and extreme-mass-ratio inspirals. In this review, motivated primarily by small-mass-ratio binaries but not limited to them, we provide an overview of essential methods in (i) black hole perturbation theory, (ii) orbital mechanics in Kerr spacetime, and (iii) gravitational self-force theory. Our treatment of black hole perturbation theory covers most common methods, including the Teukolsky and Regge-Wheeler-Zerilli equations, methods of metric reconstruction, and Lorenz-gauge formulations, casting them in a unified notation. Our treatment of orbital mechanics covers quasi-Keplerian and action-angle descriptions of bound geodesics and accelerated orbits, osculating geodesics, near-identity averaging transformations, multiscale expansions, and orbital resonances. Our summary of self-force theory's foundations is brief, covering the main ideas and results of matched asymptotic expansions, local expansion methods, puncture schemes, and point particle descriptions. We conclude by combining the above methods in a multiscale expansion of the perturbative Einstein equations, leading to adiabatic and post-adiabatic evolution and waveform-generation schemes. Our presentation includes some new results but is intended primarily as a reference for practitioners.Comment: 121 pages, 1 figure. Invited chapter for "Handbook of Gravitational Wave Astronomy" (Eds. C. Bambi, S. Katsanevas, and K. Kokkotas; Springer, Singapore, 2021). The second version corrects typos and adds Table

    Second-order perturbation theory: the problem of infinite mode coupling

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    Second-order self-force computations, which will be essential in modeling extreme-mass-ratio inspirals, involve two major new difficulties that were not present at first order. One is the problem of large scales, discussed in [Phys. Rev. D 92, 104047 (2015)]. Here we discuss the second difficulty, which occurs instead on small scales: if we expand the field equations in spherical harmonics, then because the first-order field contains a singularity, we require an arbitrarily large number of first-order modes to accurately compute even a single second-order mode. This is a generic feature of nonlinear field equations containing singularities, allowing us to study it in the simple context of a scalar toy model in flat space. Using that model, we illustrate the problem and demonstrate a robust strategy for overcoming it

    Gravitational-wave energy flux for compact binaries through second order in the mass ratio

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    Within the framework of self-force theory, we compute the gravitational-wave energy flux through second order in the mass ratio for compact binaries in quasicircular orbits. Our results are consistent with post-Newtonian calculations in the weak field and they agree remarkably well with numerical-relativity simulations of comparable-mass binaries in the strong field. We also find good agreement for binaries with a spinning secondary or a slowly spinning primary. Our results are key for accurately modelling extreme-mass-ratio inspirals and will be useful in modelling intermediate-mass-ratio systems.Comment: 5 pages + supplemental material, 7 figure

    Comparing second-order gravitational self-force and effective one body waveforms from inspiralling, quasi-circular and nonspinning black hole binaries II: the large-mass-ratio case

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    We compare recently computed waveforms from second-order gravitational self-force (GSF) theory to those generated by a new, GSF-informed, effective one body (EOB) waveform model for (spin-aligned, eccentric) inspiralling black hole binaries with large mass ratios. We focus on quasi-circular, nonspinning, configurations and perform detailed GSF/EOB waveform phasing comparisons, either in the time domain or via the gauge-invariant dimensionless function Qω≡ω2/ω˙Q_\omega\equiv \omega^2/\dot{\omega}, where ω\omega is the gravitational wave frequency. The inclusion of high-PN test-mass terms within the EOB radiation reaction (notably, up to 22PN) is crucial to achieve an EOB/GSF phasing agreement below 1~rad up to the end of the inspiral for mass ratios up to 500. For larger mass ratios, up to 5×1045\times 10^4, the contribution of horizon absorption becomes more and more important and needs to be accurately modeled. Our results indicate that our GSF-informed EOB waveform model is a promising tool to describe waveforms generated by either intermediate or extreme mass ratio inspirals for future gravitational wave detectorsComment: 13 pages, 8 figures. Submitted to Phys. Rev.

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

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    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)≡ω2/ω˙Q_\omega(\omega)\equiv \omega^2/\dot{\omega}, where ω\omega 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≤10q = m_1/m_2\le 10 TEOBResumS is largely indistinguishable from NR, 1PAT1 has a significant dephasing ≳1\gtrsim 1rad; conversely, for q≳100q\gtrsim 100, 1PAT1 is estimated to have phase errors <0.1<0.1rad on a large frequency interval, while TEOBResumS develops phase differences ≳1\gtrsim1rad with it. Most crucially, on that same large frequency interval we find good agreement between TEOBResumS and 1PAT1 in the intermediate regime 15≲q≲6415\lesssim q\lesssim 64, with <0.5<0.5rad dephasing between them. A simple modification to the TEOBResumS flux further improves this agreement for q≳30q\gtrsim 30, reducing the dephasing to ≈0.27\approx0.27rad even at q=128q=128. 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.Comment: 31 pages, 19 figures, submitted to Phys. Rev.
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