Cauchy-Characteristic Matching

Bishop, Nigel T.; Gómez, Roberto; Lehner, Luis; Szilágyi, Béla; Winicour, Jeffrey; Isaacson, Richard A.

doi:10.1007/978-94-017-0934-7_24

Cited by 46 publications

(99 citation statements)

References 17 publications

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“…Cauchy-characteristic extraction (CCE) is a method of computing gravitational radiation unambiguously and gauge-invariantly at future null infinity [27,28,57]. This method is by construction immune to uncertainties associated with finite-radius and gauge effects.…”

Section: B Cauchy-characteristic Gw Extractionmentioning

confidence: 99%

“…Metric data is propagated from the Cauchy domain onto the characteristic domain, but not vice versa. The full two-way coupling is achieved by Cauchy-characteristic matching [28,57], which has been implemented in the linearized limit in Ref. [58].…”

Section: B Cauchy-characteristic Gw Extractionmentioning

confidence: 99%

“…Following the prescription of Ref. [57], these quantities are obtained via a transformation of metric data produced by the Cauchy evolution (see below). In addition, the metric variable J is required on the initial null hypersurface.…”

Section: Characteristic Evolutionsmentioning

confidence: 99%

“…As detailed in Refs. [32,48,57], the transformation from Cauchy to characteristic metric data requires two steps. The first step involves transformation of the 4-metric from a Cartesian to an affine null coordinate system.…”

Section: Worldtube Boundary Datamentioning

confidence: 99%

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Comparing gravitational waveform extrapolation to Cauchy-characteristic extraction in binary black hole simulations

et al. 2013

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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 Ψ4 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-Ψ4 waveforms. We examine data from several different binary configurations and measure the dominant sources of error in the extrapolated-Ψ4 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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Section: B Cauchy-characteristic Gw Extractionmentioning

confidence: 99%

Section: B Cauchy-characteristic Gw Extractionmentioning

confidence: 99%

Section: Characteristic Evolutionsmentioning

confidence: 99%

Section: Worldtube Boundary Datamentioning

confidence: 99%

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Comparing gravitational waveform extrapolation to Cauchy-characteristic extraction in binary black hole simulations

et al. 2013

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“…Upon construction of proper initial data on an initial null hypersurface, which here we simply assume to be conformally flat, we have then fully specified any data necessary to evolve the fields out to J + . More details on the exact mathematical procedure can be found in [45,96]. The characteristic field equations are solved numerically using the PITT null evolution code [46].…”

Section: Cauchy-characteristic Extractionmentioning

confidence: 99%

Gravitational wave extraction in simulations of rotating stellar core collapse

et al. 2011

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We perform simulations of general relativistic rotating stellar core collapse and compute the gravitational waves (GWs) emitted in the core bounce phase of three representative models via multiple techniques. The simplest technique, the quadrupole formula (QF), estimates the GW content in the spacetime from the mass quadrupole tensor only. It is strictly valid only in the weakfield and slow-motion approximation. For the first time, we apply GW extraction methods in core collapse that are fully curvature-based and valid for strongly radiating and highly relativistic sources. These techniques are not restricted to weak-field and slow-motion assumptions. We employ three extraction methods computing (i) the Newman-Penrose (NP) scalar Ψ4, (ii) Regge-Wheeler-ZerilliMoncrief (RWZM) master functions, and (iii) Cauchy-Characteristic Extraction (CCE) allowing for the extraction of GWs at future null infinity, where the spacetime is asymptotically flat and the GW content is unambiguously defined. The latter technique is the only one not suffering from residual gauge and finite-radius effects. All curvature-based methods suffer from strong non-linear drifts. We employ the fixed-frequency integration technique as a high-pass waveform filter. Using the CCE results as a benchmark, we find that finite-radius NP extraction yields results that agree nearly perfectly in phase, but differ in amplitude by ∼ 1 − 7% at core bounce, depending on the model. RWZM waveforms, while in general agreeing in phase, contain spurious high-frequency noise of comparable amplitudes to those of the relatively weak GWs emitted in core collapse. We also find remarkably good agreement of the waveforms obtained from the QF with those obtained from CCE. The results from QF agree very well in phase and systematically underpredict peak amplitudes by ∼ 5−11%, which is comparable to the NP results and is certainly within the uncertainties associated with core collapse physics.

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A Dissipative Algorithm for Wave-like Equations in the Characteristic Formulation

Lehner

1999

Journal of Computational Physics

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We present a dissipative algorithm for solving nonlinear wave-like equations when the initial data is specified on characteristic surfaces. The dissipative properties built in this algorithm make it particularly useful when studying the highly nonlinear regime where previous methods have failed to give a stable evolution in three dimensions. The algorithm presented in this work is directly applicable to hyperbolic systems proper of electromagnetism, Yang-Mills, and general relativity theories. We carry out an analysis of the stability of the algorithm and test its properties with linear waves propagating on a Minkowski background and the scattering off a Scwharszchild black hole in general relativity.

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Cauchy-Characteristic Matching

Cited by 46 publications

References 17 publications

Comparing gravitational waveform extrapolation to Cauchy-characteristic extraction in binary black hole simulations

Comparing gravitational waveform extrapolation to Cauchy-characteristic extraction in binary black hole simulations

Gravitational wave extraction in simulations of rotating stellar core collapse

A Dissipative Algorithm for Wave-like Equations in the Characteristic Formulation

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