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Height-function-based 4D reference metrics for hyperboloidal evolution

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arxiv 2408.08952 v2 pith:3OCVRHMB submitted 2024-08-16 gr-qc

Alex Vañó-Viñuales , Tiago Valente This is my paper · ORCID
classification gr-qc
keywords hyperboloidalgaugereferenceslicesevolutionsmetricsapproachbackground
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Hyperboloidal slices are spacelike slices that reach future null infinity. Their asymptotic behaviour is different from Cauchy slices, which are traditionally used in numerical relativity simulations. This work uses free evolution of the formally-singular conformally compactified Einstein equations in spherical symmetry. One way to construct gauge conditions suitable for this approach relies on building the gauge source functions from a time-independent background spacetime metric. This background reference metric is set using the height function approach to provide the correct asymptotics of hyperboloidal slices of Minkowski spacetime. The present objective is to study the effect of different choices of height function on hyperboloidal evolutions via the reference metrics used in the gauge conditions. A total of 10 reference metrics for Minkowski are explored, identifying some of their desired features. They include 3 hyperboloidal layer constructions, evolved with the non-linear Einstein equations for the first time. Focus is put on long-term numerical stability of the evolutions, including small initial gauge perturbations. The results will be relevant for future (puncture-type) hyperboloidal evolutions, 3D simulations and the development of coinciding Cauchy and hyperboloidal data, among other applications.

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Cited by 2 Pith papers

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    First fully nonlinear Cauchy-characteristic matching simulations of binary black hole mergers are stable and accurate, and they expose late-time tails with decay exponents near -3.5 to -3.8.

  2. Semilinear wave equations in homothetic hyperboloidal coordinates and tail decay

    gr-qc 2026-08 conditional novelty 6.0 of 10

    Homothetic hyperboloidal coordinates give semilinear wave tails the same exponential decay rate at every compactified radius, removing the late-time resolution bottleneck.

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