paper

Exploring the Outer Limits of Numerical Relativity

arXiv:1304.3937 · doi:10.1103/PhysRevD.88.024001

Abstract

We perform several black-hole binary evolutions using fully nonlinear numerical relativity techniques at separations large enough that low-order post-Newtonian expansions are expected to be accurate. As a case study, we evolve an equal-mass nonspinning black-hole binary from a quasicircular orbit at an initial coordinate separation of D=100M for three different resolutions. We find that the orbital period of this binary (in the numerical coordinates) is T=6422M. The orbital motion agrees with post-Newtonian predictions to within 1%. Interestingly, we find that the time derivative of the coordinate separation is dominated by a purely gauge effect leading to an apparent contraction and expansion of the orbit at twice the orbital frequency. Based on these results, we improved our evolution techniques and studied a set of black hole binaries in quasi-circular orbits starting at D=20M, D=50M, and D=100M for ~ 5, 3, and 2 orbits, respectively. We find good agreement between the numerical results and post-Newtonian predictions for the orbital frequency and radial decay rate, radiated energy and angular momentum, and waveform amplitude and phases. The results are relevant for the future computation of long-term waveforms to assist in the detection and analysis of gravitational waves by the next generation of detectors as well as the long-term simulations of black-hole binaries required to accurately model astrophysically realistic circumbinary accretion disks.

Revised version with longer and waveforms, new plots showing omega versus proper distance, a list of orbital periods and eccentricity, and a dozen new references

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