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Register a new userExtending Gravitational Wave Extraction Using Weyl Characteristic Fields
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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.
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Gravitational waves are one of the most important diagnostic tools in the analysis of strong-gravity dynamics and have been turned into an observational channel with LIGOs detection of GW150914. Aside from their importance in astrophysics, black holes and compact matter distributions have also assumed a central role in many other branches of physics. These applications often involve spacetimes with $D>4$ dimensions where the calculation of gravitational waves is more involved than in the four dimensional case, but has now become possible thanks to substantial progress in the theoretical study of general relativity in $D>4$. Here, we develop a numerical implementation of the formalism by Godazgar and Reall (Ref.[1]) -- based on projections of the Weyl tensor analogous to the Newman-Penrose scalars -- that allows for the calculation of gravitational waves in higher dimensional spacetimes with rotational symmetry. We apply and test this method in black-hole head-on collisions from rest in $D=6$ spacetime dimensions and find that a fraction $(8.19pm 0.05)times 10^{-4}$ of the Arnowitt-Deser-Misner mass is radiated away from the system, in excellent agreement with literature results based on the Kodama-Ishibashi perturbation technique. The method presented here complements the perturbative approach by automatically including contributions from all multipoles rather than computing the energy content of individual multipoles.
We develop and calibrate a characteristic waveform extraction tool whose major improvements and corrections of pri
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.
Accurate extractions of the detected gravitational wave (GW) signal waveforms are essential to validate a detection and to probe the astrophysics behind the sources producing the GWs. This however could be difficult in realistic scenarios where the signals detected by existing GW detectors could be contaminated with non-stationary and non-Gaussian noise. While the performance of existing waveform extraction methods are optimal, they are not fast enough for online application, which is important for multi-messenger astronomy. In this paper, we demonstrate that a deep learning architecture consisting of Convolutional Neural Network and bidirectional Long Short-Term Memory components can be used to extract binary black hole (BBH) GW waveforms from realistic noise in a few milli-seconds. We have tested our network systematically on injected GW signals, with component masses uniformly distributed in the range of 10 to 80 solar masses, on Gaussian noise and LIGO detector noise. We find that our model can extract GW waveforms with overlaps of more than 0.95 with pure Numerical Relativity templates for signals with signal-to-noise ratio (SNR) greater than six, and is also robust against interfering glitches. We then apply our model to all ten detected BBH events from the first (O1) and second (O2) observation runs, obtaining greater than 0.97 overlaps for all ten extracted BBH waveforms with the corresponding pure templates. We discuss the implication of our result and its future applications to GW localization and mass estimation.
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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