Characteristic Evolution and Matching

Winicour, Jeffrey

doi:10.12942/lrr-2009-3

Cited by 52 publications

(49 citation statements)

References 236 publications

(410 reference statements)

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“…We have compared the junk radiation content for waveforms extracted at different radii, and find no significant differences. Nevertheless, it might be worthwhile to analyze the junk radiation with these effects removed through Cauchy-characteristic extraction, for instance [69,70]. …”

Section: Discussionmentioning

confidence: 99%

Including realistic tidal deformations in binary black-hole initial data

Chu

2014

Phys. Rev. D

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A shortcoming of current binary black-hole initial data is the generation of spurious gravitational radiation, so-called junk radiation, when they are evolved. This problem is a consequence of an oversimplified modeling of the binary's physics in the initial data. Since junk radiation is not astrophysically realistic, it contaminates the actual waveforms of interest and poses a numerical nuisance. The work here presents a further step towards mitigating and understanding the origin of this issue, by incorporating post-Newtonian results in the construction of constraint-satisfying binary black-hole initial data. Here we focus on including realistic tidal deformations of the black holes in the initial data, by building on the method of superposing suitably chosen black hole metrics to compute the conformal data. We describe the details of our initial data for an equal-mass and nonspinning binary, compute the subsequent relaxation of horizon quantities in evolutions, and quantify the amount of junk radiation that is generated. These results are contrasted with those obtained with the most common choice of conformally flat (CF) initial data, as well as superposed Kerr-Schild (SKS) initial data. We find that when realistic tidal deformations are included, the early transients in the horizon geometries are significantly reduced, along with smaller deviations in the relaxed black hole masses and spins from their starting values. Likewise, the junk radiation content in the l = 2 modes is reduced by a factor of ∼1.7 relative to CF initial data, but only by a factor of ∼1.2 relative to SKS initial data. More prominently, the junk radiation content in the 3 ≤ l ≤ 8 modes is reduced by a factor of ∼5 relative to CF initial data, and by a factor of ∼2.4 relative to SKS initial data.

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Section: Discussionmentioning

confidence: 99%

Including realistic tidal deformations in binary black-hole initial data

Chu

2014

Phys. Rev. D

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“…The use of multi-block methods in BSSN simulations [93,94] allows to make use of spherical wavezone grids to take advantage of topologically adapted grids, but they keep a cartesian grid in the central region. On the other hand, spherical coordinates are widely used in the null formulations (see [28]), mostly in the context of Cauchy-characteristic matching and extraction (e.g. [29][30][31]), although stand-alone characteristic formulations have still very few numerical applications (e.g.…”

Section: Discussionmentioning

confidence: 99%

“…Within the 3+1 decomposition of Einstein equations, some formulations have appeared [15,27] in order to try to improve some of the weaknesses of the BSSN formulation, such as a better preservation of the constraints. An alternative is the characteristic approach (see [28] for a review). The Cauchy-characteristic matching and extraction, based on a (2+1)+1 formulation, has been successfully used to accurately extract gravitational waves matching its evolution to interior Cauchy data [29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Gravitational waves in dynamical spacetimes with matter content in the fully constrained formulation

Cordero-Carrión

Cerdá–Durán²,

Ibáñez³

2012

Phys. Rev. D

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The Fully Constrained Formulation (FCF) of General Relativity (GR) is a framework introduced as an alternative to the hyperbolic formulations traditionally used in numerical relativity. The FCF equations form a hybrid elliptic-hyperbolic system of equations including explicitly the constraints. We present an implicit-explicit numerical algorithm to solve the hyperbolic part, whereas the elliptic sector shares the form and properties with the well known Conformally Flat Condition (CFC) approximation. We show the stability and convergence properties of the numerical scheme with numerical simulations of vacuum solutions. We have performed the first numerical evolutions of the coupled system of hydrodynamics and Einstein equations within FCF. As a proof of principle of the viability of the formalism, we present 2D axisymmetric simulations of an oscillating neutron star. In order to simplify the analysis we have neglected the back-reaction of the gravitational waves (GWs) into the dynamics, which is small (< 2%) for the system considered in this work. We use spherical coordinates grids which are well adapted for simulations of stars and allow for extended grids that marginally reach the wave zone. We have extracted the GW signature and compared to the Newtonian quadrupole and hexadecapole formulae. Both extraction methods show agreement within the numerical errors and the approximations used (∼ 30%).

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“…2. Briefly, for second order global accuracy I use a standard diamond-cell integration scheme [16,33,34,37,55,56,84], while for fourth order global accuracy I use a modified version of the scheme described by Lousto [55] and Haas [38]. I describe the finite differencing schemes in detail in Appendix A.…”

Section: Unigrid Finite Differencingmentioning

confidence: 99%

“…To discretize the wave equation (3) to second order global accuracy in the grid spacing , I use a standard diamond-cell integration scheme [16,33,34,37,55,56,84]:…”

Section: Appendix A: Details Of the Unigrid Finite Differencing Schemementioning

confidence: 99%

Adaptive mesh refinement for characteristic grids

Thornburg

2010

Gen Relativ Gravit

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I consider techniques for Berger-Oliger adaptive mesh refinement (AMR) when numerically solving partial differential equations with wave-like solutions, using characteristic (double-null) grids. Such AMR algorithms are naturally recursive, and the best-known past Berger-Oliger characteristic AMR algorithm, that of Pretorius and Lehner (J Comp Phys 198:10, 2004), recurses on individual "diamond" characteristic grid cells. This leads to the use of fine-grained memory management, with individual grid cells kept in two-dimensional linked lists at each refinement level. This complicates the implementation and adds overhead in both space and time. Here I describe a Berger-Oliger characteristic AMR algorithm which instead recurses on null slices. This algorithm is very similar to the usual Cauchy Berger-Oliger algorithm, and uses relatively coarse-grained memory management, allowing entire null slices to be stored in contiguous arrays in memory. The algorithm is very efficient in both space and time. I describe discretizations yielding both second and fourth order global accuracy. My code implementing the algorithm described here is included in the electronic supplementary materials accompanying this paper, and is freely available to other researchers under the terms of the GNU general public license. This paper is dedicated to the memory of Thomas Radke, my late friend and colleague in many computational adventures. Electronic supplementary materialThe online version of this article (

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Characteristic Evolution and Matching

Cited by 52 publications

References 236 publications

Including realistic tidal deformations in binary black-hole initial data

Including realistic tidal deformations in binary black-hole initial data

Gravitational waves in dynamical spacetimes with matter content in the fully constrained formulation

Adaptive mesh refinement for characteristic grids

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