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Register a new userA Characteristic Extraction Tool for Gravitational Waveforms
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We develop and calibrate a characteristic waveform extraction tool whose major improvements and corrections of pri
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We develop, test and compare new numerical and geometrical methods for improving the accuracy of extracting waveforms using characteristic evolution. The new numerical method involves use of circular boundaries to the stereographic grid patches which cover the spherical cross-sections of the outgoing null cones. We show how an angular version of numerical dissipation can be introduced into the characteristic code to damp the high frequency error arising form the irregular way the circular patch boundary cuts through the grid. The new geometric method involves use of the Weyl tensor component $Psi_4$ to extract the waveform as opposed to the original approach via the Bondi news function. We develop the necessary analytic and computational formula to compute the $O(1/r)$ radiative part of $Psi_4$ in terms of a conformally compactified treatment of null infinity. These methods are compared and calibrated in test problems based upon linearized waves.
We present a detailed methodology for extracting the full set of Newman-Penrose Weyl scalars from numerically generated spacetimes without requiring a tetrad that is completely orthonormal or perfectly aligned to the principal null directions. We also describe how to implement an extrapolation technique for computing the Weyl scalars contribution at asymptotic null infinity in postprocessing. These methods have been used to produce $Psi_4$ and $h$ waveforms for the Simulating eXtreme Spacetimes (SXS) waveform catalog and now have been expanded to produce the entire set of Weyl scalars. These new waveform quantities are critical for the future of gravitational wave astronomy in order to understand the finite-amplitude gauge differences that can occur in numerical waveforms. We also present a new analysis of the accuracy of waveforms produced by the Spectral Einstein Code. While ultimately we expect Cauchy characteristic extraction to yield more accurate waveforms, the extraction techniques described here are far easier to implement and have already proven to be a viable way to produce production-level waveforms that can meet the demands of current gravitational-wave detectors.
The accurate modeling of gravitational radiation is a key issue for gravitational wave astronomy. As simulation codes reach higher accuracy, systematic errors inherent in current numerical relativity wave-extraction methods become evident, and may lead to a wrong astrophysical interpretation of the data. In this paper, we give a detailed description of the Cauchy-characteristic extraction technique applied to binary black hole inspiral and merger evolutions to obtain gravitational waveforms that are defined unambiguously, that is, at future null infinity. By this method we remove finite-radius approximations and the need to extrapolate data from the near zone. Further, we demonstrate that the method is free of gauge effects and thus is affected only by numerical error. Various consistency checks reveal that energy and angular momentum are conserved to high precision and agree very well with extrapolated data. In addition, we revisit the computation of the gravitational recoil and find that finite radius extrapolation very well approximates the result at $scri$. However, the (non-convergent) systematic differences to extrapolated data are of the same order of magnitude as the (convergent) discretisation error of the Cauchy evolution hence highlighting the need for correct wave-extraction.
We present several improvements to the Cauchy-characteristic evolution procedure that generates high-fidelity gravitational waveforms at $mathcal{I}^+$ from numerical relativity simulations. Cauchy-characteristic evolution combines an interior solution of the Einstein field equations based on Cauchy slices with an exterior solution based on null slices that extend to $mathcal{I}^+$. The foundation of our improved algorithm is a comprehensive method of handling the gauge transformations between the arbitrarily specified coordinates of the interior Cauchy evolution and the unique (up to BMS transformations) Bondi-Sachs coordinate system of the exterior characteristic evolution. We present a reformulated set of characteristic evolution equations better adapted to numerical implementation. In addition, we develop a method to ensure that the angular coordinates used in the volume during the characteristic evolution are asymptotically inertial. This provides a direct route to an expanded set of waveform outputs and is guaranteed to avoid pure-gauge logarithmic dependence that has caused trouble for previous spectral implementations of the characteristic evolution equations. We construct a set of Weyl scalars compatible with the Bondi-like coordinate systems used in characteristic evolution, and determine simple, easily implemented forms for the asymptotic Weyl scalars in our suggested set of coordinates.
We extract gravitational waveforms from numerical simulations of black hole binaries computed using the Spectral Einstein Code. We compare two extraction methods: direct construction of the Newman-Penrose (NP) scalar $Psi_4$ at a finite distance from the source and Cauchy-characteristic extraction (CCE). The direct NP approach is simpler than CCE, but NP waveforms can be contaminated by near-zone effects---unless the waves are extracted at several distances from the source and extrapolated to infinity. Even then, the resulting waveforms can in principle be contaminated by gauge effects. In contrast, CCE directly provides, by construction, gauge-invariant waveforms at future null infinity. We verify the gauge invariance of CCE by running the same physical simulation using two different gauge conditions. We find that these two gauge conditions produce the same CCE waveforms but show differences in extrapolated-$Psi_4$ waveforms. We examine data from several different binary configurations and measure the dominant sources of error in the extrapolated-$Psi_4$ and CCE waveforms. In some cases, we find that NP waveforms extrapolated to infinity agree with the corresponding CCE waveforms to within the estimated error bars. However, we find that in other cases extrapolated and CCE waveforms disagree, most notably for $m=0$ memory modes.
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