Asymptotics of solutions of a hyperbolic formulation of the constraint equations

Beyer, Florian; Escobar, Luis; Frauendiener, Jörg

doi:10.1088/1361-6382/aa8be6

Cited by 10 publications

(59 citation statements)

References 38 publications

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“…With no control over the asymptotics it is therefore possible that the method generates initial data sets that lack a physical interpretation. Exactly this issue has been explored recently in [10,12,19]. It was confirmed that generic solutions of these equations are not asymptotically flat (this notion is defined in Section 4 below).…”

Section: Introductionmentioning

confidence: 90%

“…In this subsection we introduce data sets (without imposing the constraints yet) of Kerr-Schild form. Such data sets were the basis of our previous work in [10,12] and we shall continue to use them in particular in Section 6.1. In this paper now we introduce such data sets as follows.…”

Section: Kerr-schild-like Data Setsmentioning

confidence: 99%

“…In all of what follows we shall assume without further notice that ρ − is sufficiently large so that all 2 + 1-quantities are well-defined. Recall that asymptotically flat data sets have been studied by us before in [10,12] where we have we used the same definitions originally from [20].…”

Section: )mentioning

confidence: 99%

“…Since the exterior region is foliated by 2-spheres, we can apply the spin-weight formalism following [7][8][9][10][11]29]. A brief summary is given in Section A in the appendix.…”

Section: Numerical Setupmentioning

confidence: 99%

“…This will allow us to use the same numerical pseudo-spectral methods developed in [6,8,9,11] based on the ð-and the spinweight formalism. As in [10,12], our focus is on the asymptotics exclusively. In particular, we are not concerned with the properties of the solutions in the strong field regime, e.g.…”

Section: Introductionmentioning

confidence: 99%

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Asymptotically flat vacuum initial data sets from a modified parabolic-hyperbolic formulation of the Einstein vacuum constraint equations

2020

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In this paper we continue earlier investigations [10,12,19] of evolutionary formulations of the Einstein vacuum constraint equations originally introduced by Rácz. Motivated by the strong evidence from these works that the resulting vacuum initial data sets are generically not asymptotically flat we analyse the asymptotics of the solutions of a modified formulation by a combination of analytical and numerical techniques. We conclude that the vacuum initial data sets generated with this new formulation are generically asymptotically flat. *

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Section: Introductionmentioning

confidence: 90%

Section: Kerr-schild-like Data Setsmentioning

confidence: 99%

Section: )mentioning

confidence: 99%

“…Since the exterior region is foliated by 2-spheres, we can apply the spin-weight formalism following [7][8][9][10][11]29]. A brief summary is given in Section A in the appendix.…”

Section: Numerical Setupmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Asymptotically flat vacuum initial data sets from a modified parabolic-hyperbolic formulation of the Einstein vacuum constraint equations

2020

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Toward computing gravitational initial data without elliptic solvers

Rácz¹,

Winicour²

2018

Class. Quantum Grav.

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Two new methods have been proposed for solving the gravitational constraints without using elliptic solvers by formulating them as either an algebraichyperbolic or parabolic-hyperbolic system. Here, we compare these two methods and present a unified computational infrastructure for their implementation as numerical evolution codes. An important potential application of these methods is the prescription of initial data for the simulation of black holes. This paper is meant to support progress and activity in that direction.

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Numerical construction of initial data sets of binary black hole type using a parabolic-hyperbolic formulation of the vacuum constraint equations

Beyer

Escobar

Frauendiener

et al. 2019

Class. Quantum Grav.

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In this paper we investigate the parabolic-hyperbolic formulation of the vacuum constraint equations introduced by Rácz with a view to constructing multiple black hole initial data sets without spin. In order to respect the natural properties of this configuration, we foliate the spatial domain with 2-spheres. It is then a consequence of these equations that they must be solved as an initial value problem evolving outwards towards spacelike infinity. Choosing the free data and the "strong field boundary conditions" for these equations in a way which mimics asymptotically flat and asymptotically spherical binary black hole initial data sets, our focus in this paper is on the analysis of the asymptotics of the solutions. In agreement with our earlier results, our combination of analytical and numerical tools reveals that these solutions are in general not asymptotically flat, but have a cone geometry instead. In order to remedy this and approximate asymptotically Euclidean data sets, we then propose and test an iterative numerical scheme. *

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Asymptotics of solutions of a hyperbolic formulation of the constraint equations

Cited by 10 publications

References 38 publications

Asymptotically flat vacuum initial data sets from a modified parabolic-hyperbolic formulation of the Einstein vacuum constraint equations

Asymptotically flat vacuum initial data sets from a modified parabolic-hyperbolic formulation of the Einstein vacuum constraint equations

Toward computing gravitational initial data without elliptic solvers

Numerical construction of initial data sets of binary black hole type using a parabolic-hyperbolic formulation of the vacuum constraint equations

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