Constraint-preserving boundary treatment for a harmonic formulation of the Einstein equations

Seiler, Jennifer; Szilágyi, Béla; Pollney, Denis; Rezzolla, Luciano

doi:10.1088/0264-9381/25/17/175020

Cited by 37 publications

(22 citation statements)

References 41 publications

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“…The most common way to incorporate this freedom is to rescale all dimensionful quantities by the mass M. In particular, Eq. (14) can be written in terms of the dimensionless variables r=M, KM, and C=M 2 as…”

Section: Minimal Surfaces and Trumpetsmentioning

confidence: 99%

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Black hole initial data on hyperboloidal slices

2009

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We generalize Bowen-York black hole initial data to hyperboloidal constant mean curvature slices which extend to future null infinity. We solve this initial value problem numerically for several cases, including unequal mass binary black holes with spins and boosts. The singularity at null infinity in the Hamiltonian constraint associated with a constant mean curvature hypersurface does not pose any particular difficulties. The inner boundaries of our slices are minimal surfaces. Trumpet configurations are explored both analytically and numerically.Comment: version for publication in Phys. Rev.

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Section: Minimal Surfaces and Trumpetsmentioning

confidence: 99%

“…Additionally, extending the simulation to I þ would make it unnecessary to deal with gravitational wave extraction at a finite distance, or with artificial outer boundaries on a truncated domain, two very complicated aspects of black hole simulations (see, e.g. [5][6][7][8][9][10][11][12][13][14]). …”

Section: Introductionmentioning

confidence: 99%

Black hole initial data on hyperboloidal slices

2009

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“…A Cauchy evolution code, the Abigel code, based upon a discretized version of these energy estimates was found to be stable, convergent and constraint preserving in nonlinear boundary tests [14]. These results were confirmed using an independent harmonic code developed at the Albert Einstein Institute [266]. A linearized version of the Abigel code has been used to successfully carry out CCM (see Section 5.8).…”

Section: Cauchy-characteristic Matchingmentioning

confidence: 92%

Characteristic Evolution and Matching

Winicour

2012

Living Rev. Relativ.

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I review the development of numerical evolution codes for general relativity based upon the characteristic initial-value problem. Progress in characteristic evolution is traced from the early stage of 1D feasibility studies to 2D-axisymmetric codes that accurately simulate the oscillations and gravitational collapse of relativistic stars and to current 3D codes that provide pieces of a binary black-hole spacetime. Cauchy codes have now been successful at simulating all aspects of the binary black-hole problem inside an artificially constructed outer boundary. A prime application of characteristic evolution is to extend such simulations to null infinity where the waveform from the binary inspiral and merger can be unambiguously computed. This has now been accomplished by Cauchy-characteristic extraction, where data for the characteristic evolution is supplied by Cauchy data on an extraction worldtube inside the artificial outer boundary. The ultimate application of characteristic evolution is to eliminate the role of this outer boundary by constructing a global solution via Cauchy-characteristic matching. Progress in this direction is discussed.

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“…A strong motivation for the hyperboloidal approach is to improve the accuracy and efficiency of numerical relativistic calculations of binary black holes where the outer boundary and the radiation extraction problems have distinctive features [17][18][19][20][21][22][23][24]. There is an ongoing effort to solve a hyperboloidal initial value problem for various versions of the Einstein equations [25][26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Hyperboloidal evolution of test fields in three spatial dimensions

Zenginoğlu

Kidder

2010

Phys. Rev. D

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We present the numerical implementation of a clean solution to the outer boundary and radiation extraction problems within the 3+1 formalism for hyperbolic partial differential equations on a given background. Our approach is based on compactification at null infinity in hyperboloidal scri fixing coordinates. We report numerical tests for the particular example of a scalar wave equation on Minkowski and Schwarzschild backgrounds. We address issues related to the implementation of the hyperboloidal approach for the Einstein equations, such as nonlinear source functions, matching, and evaluation of formally singular terms at null infinity.Comment: 10 pages, 8 figure

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Constraint-preserving boundary treatment for a harmonic formulation of the Einstein equations

Cited by 37 publications

References 41 publications

Black hole initial data on hyperboloidal slices

Black hole initial data on hyperboloidal slices

Characteristic Evolution and Matching

Hyperboloidal evolution of test fields in three spatial dimensions

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