General relativistic null-cone evolutions with a high-order scheme

Reisswig, Christian; Bishop, Nigel T.; Pollney, Denis

doi:10.1007/s10714-013-1513-1

Cited by 22 publications

(23 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Gravitational wave extraction is done by three independent methods: direct extraction of the Newman-Penrose quantity Ψ 4 at finite radius [48,76,84], extraction of the strain h by matching to solutions of the Regge-Wheeler-Zerilli-Moncrief equations at finite radius [85,86], and Cauchy-Characteristic Extraction [87][88][89][90][91]. The latter method directly provides gravitational waveforms at future null infinity, while for the former two methods the waveforms are computed at a series of finite radii and then extrapolated to infinity [92].…”

Section: Simulations Using Pseudospectral Excision Methodsmentioning

confidence: 99%

Modeling the source of GW150914 with targeted numerical-relativity simulations

Lovelace

Loustó

Healy

et al. 2016

Class. Quantum Grav.

120

View full text Add to dashboard Cite

In fall of 2015, the two LIGO detectors measured the gravitational wave signal GW150914, which originated from a pair of merging black holes [1]. In the final 0.2 seconds (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 [2]. 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.

show abstract

Section: Simulations Using Pseudospectral Excision Methodsmentioning

confidence: 99%

Modeling the source of GW150914 with targeted numerical-relativity simulations

Lovelace

Loustó

Healy

et al. 2016

Class. Quantum Grav.

120

View full text Add to dashboard Cite

show abstract

“…Comparison with Cauchy Characteristic Extraction, or CCE, an alternative which applies Characteristic Evolution to enable waveform computation at future null infinity, suggests that extrapolation gauge errors could dominate the global error [12]. Characteristic Evolution has been previously implemented at up to 4 th order radial accuracy [13], while complete extraction has been achieved with finite difference/volume methods up to 2 nd order [14,15]. Here we implement inner boundary extraction and evolution.…”

mentioning

confidence: 99%

Spectral characteristic evolution: a new algorithm for gravitational wave propagation

Handmer

Szilágyi²

2014

Class. Quantum Grav.

View full text Add to dashboard Cite

Abstract. We present a spectral algorithm for solving the full nonlinear vacuum Einstein field equations in the Bondi framework. Developed within the Spectral Einstein Code (SpEC), we demonstrate spectral characteristic evolution as a technical precursor to Cauchy Characteristic Extraction (CCE), a rigorous method for obtaining gauge-invariant gravitational waveforms from existing and future astrophysical simulations. We demonstrate the new algorithm's stability, convergence, and agreement with existing evolution methods. We explain how an innovative spectral approach enables a two orders of magnitude improvement in computational efficiency. What is Characteristic Evolution, and why?As an international network of gravitational wave observatories come online, the race to the first direct detection of gravitational waves is expected to herald the beginning of gravitational wave astronomy. Detectors such as Advanced LIGO, VIRGO, GEO, and KAGRA aim for strain sensitivities approaching 10 −24 [1,2,3,4]. Nevertheless, signal candidates from compact binaries or supernovae will be on the cusp of detectability, with very poor signal to noise ratios requiring matched filtering for detection [5]. Matched filtering requires a comprehensive template bank, the generation of which has been a primary goal of the field of numerical relativity. These templates cover a range of expected astronomical phenomena, and are generated by a variety of numerical codes, including the Spectral Einstein Code (SpEC) [6]. Filling out the template bank requires a balance of numerical relativity and analytic waveforms and effective-one-body[8]), with waveform models often calibrated using numerical results [9,10,11].One technical challenge facing the construction of a large template bank is extraction of gauge invariant waveforms from simulations. In general, large computationally intensive simulations are needed to describe the physics of events such as supernovae and compact object binary inspirals. While a waveform-like signal can readily be extracted from arXiv:1406.7029v2 [gr-qc] 24 Sep 2014 anywhere in the computational domain, waveforms are only rigorously defined at future null infinity. Finite radii waveform approximations are universally contaminated by coordinate system dynamics, or gauge effects, which are poorly understood and nearly impossible to remove or even quantify. Comparison with Cauchy Characteristic Extraction, or CCE, an alternative which applies Characteristic Evolution to enable waveform computation at future null infinity, suggests that extrapolation gauge errors could dominate the global error [12]. Characteristic Evolution has been previously implemented at up to 4 th order radial accuracy [13], while complete extraction has been achieved with finite difference/volume methods up to 2 nd order [14,15]. Here we implement inner boundary extraction and evolution. This must be combined with an appropriate outer boundary algorithm to generate the gauge-invariant news at future null infinity. In a hypothetical complete ...

show abstract

“…where we have used the definition (135) to derive the right-hand side of expression (194). As a result, the asymptotic relation between the two components of the even-parity part of the perturbation metric simply reads…”

Section: Asymptotic Expressions From Even-parity Perturbationsmentioning

confidence: 99%

“…The early work that eventually led to the PITT code was for the case of axisymmetry [134,52,121], and a general vacuum code was developed in the mid-1990s [57,54,146,147,149]. Subsequently, the code was extended to the non-vacuum case [55,56], and code adaptations in terms of variables, coordinates and order of accuracy have been investigated [117,118,193,194]. Spectral, rather than finite difference, implementations have also been developed, for both the axially symmetric case [93] and in general [126].…”

Section: Gravitational Waves In the Characteristic Approachmentioning

confidence: 99%

Extraction of gravitational waves in numerical relativity

Bishop¹,

Rezzolla²

2016

Living Rev Relativ

131

108

View full text Add to dashboard Cite

A numerical-relativity calculation yields in general a solution of the Einstein equations including also a radiative part, which is in practice computed in a region of finite extent. Since gravitational radiation is properly defined only at null infinity and in an appropriate coordinate system, the accurate estimation of the emitted gravitational waves represents an old and non-trivial problem in numerical relativity. A number of methods have been developed over the years to “extract” the radiative part of the solution from a numerical simulation and these include: quadrupole formulas, gauge-invariant metric perturbations, Weyl scalars, and characteristic extraction. We review and discuss each method, in terms of both its theoretical background as well as its implementation. Finally, we provide a brief comparison of the various methods in terms of their inherent advantages and disadvantages.Electronic supplementary materialThe online version of this article (doi:10.1007/s41114-016-0001-9) contains supplementary material, which is available to authorized users.

show abstract

General relativistic null-cone evolutions with a high-order scheme

Cited by 22 publications

References 33 publications

Modeling the source of GW150914 with targeted numerical-relativity simulations

Modeling the source of GW150914 with targeted numerical-relativity simulations

Spectral characteristic evolution: a new algorithm for gravitational wave propagation

Extraction of gravitational waves in numerical relativity

Contact Info

Product

Resources

About