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In fall of 2015, the two LIGO detectors measured the gravitational wave signal GW150914, which originated from a pair of merging black holes (Abbott et al Virgo, LIGO Scientific 2016 Phys. Rev. Lett. 116 061102). In the final 0.2 s (about 8 gravitational-wave cycles) before the amplitude reached its maximum, the observed signal swept up in amplitude and frequency, from 35 Hz to 150 Hz. The theoretical gravitational-wave signal for merging black holes, as predicted by general relativity, can be computed only by full numerical relativity, because analytic approximations fail near the time of merger. Moreover, the nearly-equal masses, moderate spins, and small number of orbits of GW150914 are especially straightforward and efficient to simulate with modern numerical-relativity codes. In this paper, we report the modeling of GW150914 with numerical-relativity simulations, using black-hole masses and spins consistent with those inferred from LIGO’s measurement (Abbott et al LIGO Scientific Collaboration, Virgo Collaboration 2016 Phys. Rev. Lett. 116 241102). In particular, we employ two independent numerical-relativity codes that use completely different analytical and numerical methods to model the same merging black holes and to compute the emitted gravitational waveform; we find excellent agreement between the waveforms produced by the two independent codes. These results demonstrate the validity, impact, and potential of current and future studies using rapid-response, targeted numerical-relativity simulations for better understanding gravitational-wave observations. [ABSTRACT FROM AUTHOR]

We present a new set of 95 numerical relativity simulations of non-precessing binary black holes (BBHs). The simulations sample comprehensively both black-hole spins up to spin magnitude of 0.9, and cover mass ratios 1–3. The simulations cover on average 24 inspiral orbits, plus merger and ringdown, with low initial orbital eccentricities . A subset of the simulations extends the coverage of non-spinning BBHs up to mass ratio q = 10. Gravitational waveforms at asymptotic infinity are computed with two independent techniques: extrapolation and Cauchy characteristic extraction. An error analysis based on noise-weighted inner products is performed. We find that numerical truncation error, error due to gravitational wave extraction, and errors due to the Fourier transformation of signals with finite length of the numerical waveforms are of similar magnitude, with gravitational wave extraction errors dominating at noise-weighted mismatches of . This set of waveforms will serve to validate and improve aligned-spin waveform models for gravitational wave science. [ABSTRACT FROM AUTHOR]

Astrophysical black holes could be nearly extremal (that is, rotating nearly as fast as possible); therefore, nearly extremal black holes could be among the binaries that current and future gravitational-wave observatories will detect. Predicting the gravitational waves emitted by merging black holes requires numerical-relativity simulations, but these simulations are especially challenging when one or both holes have mass m and spin S exceeding the Bowen–York limit of . We present improved methods that enable us to simulate merging, nearly extremal black holes (i.e., black holes with ) more robustly and more efficiently. We use these methods to simulate an unequal-mass, precessing binary black hole (BBH) coalescence, where the larger black hole has . We also use these methods to simulate a non-precessing BBH coalescence, where both black holes have , nearly reaching the Novikov–Thorne upper bound for holes spun up by thin accretion disks. We demonstrate numerical convergence and estimate the numerical errors of the waveforms; we compare numerical waveforms from our simulations with post-Newtonian and effective-one-body waveforms; we compare the evolution of the black hole masses and spins with analytic predictions; and we explore the effect of increasing spin magnitude on the orbital dynamics (the so-called ‘orbital hangup’ effect). [ABSTRACT FROM AUTHOR]

The spin angular momentum S of an isolated Kerr black hole is bounded by the surface area A of its apparent horizon: , with equality for extremal black holes. In this paper, we explore the extremality of individual and common apparent horizons for merging, rapidly spinning binary black holes. We consider simulations of merging black holes with equal masses M and initial spin angular momenta aligned with the orbital angular momentum, including new simulations with spin magnitudes up to . We measure the area and (using approximate Killing vectors) the spin on the individual and common apparent horizons, finding that the inequality is satisfied in all cases but is very close to equality on the common apparent horizon at the instant it first appears. We also evaluate the Booth–Fairhurst extremality, whose value for a given apparent horizon depends on the scaling of the horizon’s null normal vectors. In particular, we introduce a gauge-invariant lower bound on the extremality by computing the smallest value that Booth and Fairhurst’s extremality parameter can take for any scaling. Using this lower bound, we conclude that the common horizons are at least moderately close to extremal just after they appear. Finally, following Lovelace et al (2008 Phys. Rev. D78 084017), we construct quasiequilibrium binary-black hole initial data with ‘overspun’ marginally trapped surfaces with . We show that the overspun surfaces are indeed superextremal: our lower bound on their Booth–Fairhurst extremality exceeds unity. However, we confirm that these superextremal surfaces are always surrounded by marginally outer trapped surfaces (i.e., by apparent horizons) with . The extremality lower bound on the enclosing apparent horizon is always less than unity but can exceed the value for an extremal Kerr black hole. [ABSTRACT FROM AUTHOR]