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      Binary black hole coalescence in the extreme-mass-ratio limit: testing and improving the effective-one-body multipolar waveform

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          Abstract

          We discuss the properties of the effective-one-body (EOB) multipolar gravitational waveform emitted by nonspinning black-hole binaries of masses \(\mu\) and \(M\) in the extreme-mass-ratio limit, \(\mu/M=\nu\ll 1\). We focus on the transition from quasicircular inspiral to plunge, merger and ringdown.We compare the EOB waveform to a Regge-Wheeler-Zerilli (RWZ) waveform computed using the hyperboloidal layer method and extracted at null infinity. Because the EOB waveform keeps track analytically of most phase differences in the early inspiral, we do not allow for any arbitrary time or phase shift between the waveforms. The dynamics of the particle, common to both wave-generation formalisms, is driven by leading-order \({\cal O}(\nu)\) analytically--resummed radiation reaction. The EOB and the RWZ waveforms have an initial dephasing of about \(5\times 10^{-4}\) rad and maintain then a remarkably accurate phase coherence during the long inspiral (\(\sim 33\) orbits), accumulating only about \(-2\times 10^{-3}\) rad until the last stable orbit, i.e. \(\Delta\phi/\phi\sim -5.95\times 10^{-6}\). We obtain such accuracy without calibrating the analytically-resummed EOB waveform to numerical data, which indicates the aptitude of the EOB waveform for LISA-oriented studies. We then improve the behavior of the EOB waveform around merger by introducing and tuning next-to-quasi-circular corrections both in the gravitational wave amplitude and phase. For each multipole we tune only four next-to-quasi-circular parameters by requiring compatibility between EOB and RWZ waveforms at the light-ring. The resulting phase difference around merger time is as small as \(\pm 0.015\) rad, with a fractional amplitude agreement of 2.5%. This suggest that next-to-quasi-circular corrections to the phase can be a useful ingredient in comparisons between EOB and numerical relativity waveforms.

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          Most cited references39

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          Stability of a Schwarzschild Singularity

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            Evolution of Binary Black Hole Spacetimes

            We describe early success in the evolution of binary black hole spacetimes with a numerical code based on a generalization of harmonic coordinates. Indications are that with sufficient resolution this scheme is capable of evolving binary systems for enough time to extract information about the orbit, merger and gravitational waves emitted during the event. As an example we show results from the evolution of a binary composed of two equal mass, non-spinning black holes, through a single plunge-orbit, merger and ring down. The resultant black hole is estimated to be a Kerr black hole with angular momentum parameter a~0.70. At present, lack of resolution far from the binary prevents an accurate estimate of the energy emitted, though a rough calculation suggests on the order of 5% of the initial rest mass of the system is radiated as gravitational waves during the final orbit and ringdown.
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              Effective one-body approach to general relativistic two-body dynamics

              We map the general relativistic two-body problem onto that of a test particle moving in an effective external metric. This effective-one-body approach defines, in a non-perturbative manner, the late dynamical evolution of a coalescing binary system of compact objects. The transition from the adiabatic inspiral, driven by gravitational radiation damping, to an unstable plunge, induced by strong spacetime curvature, is predicted to occur for orbits more tightly bound than the innermost stable circular orbit in a Schwarzschild metric of mass M = m1 + m2. The binding energy, angular momentum and orbital frequency of the innermost stable circular orbit for the time-symmetric two-body problem are determined as a function of the mass ratio.
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                Author and article information

                Journal
                11 December 2010
                2011-03-10
                Article
                10.1103/PhysRevD.83.064010
                1012.2456
                9fae6481-29c3-48dd-a0e5-eae6fd390822

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                Phys.Rev.D83:064010,2011
                gr-qc astro-ph.CO

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