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Numerical Calculation of Conformally Smooth Hyperboloidal Data
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This is the third paper in a series describing a numerical implementation of the conformal Einstein equation. This paper describes a scheme to calculate (three) dimensional data for the conformal field equations from a set of free functions. The actual implementation depends on the topology of the spacetime. We discuss the implementation and exemplary calculations for data leading to spacetimes with one spherical null infinity (asymptotically Minkowski) and for data leading to spacetimes with two toroidal null infinities (asymptotically A3). We also outline the (technical) modifications of the implementation needed to calculate data for spacetimes with two and more spherical null infinities (asymptotically Schwarzschild and asymptotically multiple black holes).
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Cited by 2 Pith papers
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3d Summation-by-Parts scheme for Linear Wave Equations on Hyperboloidal Slices
Derives a provably stable 3D SBP scheme for linear waves on hyperboloidal slices using compactification, rescaling, and abstract dissipation in spherical polar coordinates.
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Conformal compactification and affine-null metric formulation of the Einstein equations
A hierarchical, boundary-regular affine-null form of the conformal Einstein-scalar equations is derived, shown equivalent to compactified physical-space equations, and used to extract the news function at null infinity.
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