Numerical stability of the Hyperbolic Formulation of the Constraint equations for $\mathbb{T}^3$ cosmological space-times

[2309.02946] Numerical stability of the Hyperbolic Formulation of the Constraint equations for $\mathbb{T}^3$ cosmological space-times Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search General Relativity and Quantum Cosmology arXiv:2309.02946 (gr-qc) [Submitted on 6 Sep 2023 ( v1 ), last revised 15 Apr 2026 (this version, v5)] Title: Numerical stability of the Hyperbolic Formulation of the Constraint equations for $\mathbb{T}^3$ cosmological space-times Authors: Alejandro Estrada-Llesta , Cristhian Martinez-Duarte , Leon Escobar-Diaz View a PDF of the paper titled Numerical stability of the Hyperbolic Formulation of the Constraint equations for $\mathbb{T}^3$ cosmological space-times, by Alejandro Estrada-Llesta and 1 other authors View PDF HTML (experimental) Abstract: In this work, we study of the algebraic-hyperbolic formulation of the Einstein constraint equations for numerically constructing initial data sets for inhomogeneous cosmological space-times with $\mathbb{T}^3$ topology. We implement a pseudo-spectral method of lines based on the discrete Fourier transform and find that the scheme exhibits pathological instabilities. Through linear stability analysis, we prove that the instabilities are unavoidable for any space-time sufficiently close to FLRW while we find that this approach can be stable for Gowdy space-times depending on the initial time choice. Additionally, we present numerical evidence that certain subclasses of the algebraic-hyperbolic formulation, when combined with a Fourier-based method of lines, are numerically stable, thus offering a potential new path for computing initial data sets for inhomogeneous cosmological space-times. Comments: 39 pages, 20 figures Subjects: General Relativity and Quantum Cosmology (gr-qc) Cite as: arXiv:2309.02946 [gr-qc] (or arXiv:2309.02946v5 [gr-qc] for this version) https://doi.org/10.48550/arXiv.2309.02946 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Alejandro Estrada-Llesta [ view email ] [v1] Wed, 6 Sep 2023 12:25:40 UTC (1,568 KB) [v2] Wed, 13 Aug 2025 08:58:49 UTC (1,907 KB) [v3] Thu, 18 Dec 2025 14:17:05 UTC (1,700 KB) [v4] Tue, 14 Apr 2026 05:52:05 UTC (1,704 KB) [v5] Wed, 15 Apr 2026 10:37:40 UTC (1,697 KB) Full-text links: Access Paper: View a PDF of the paper titled Numerical stability of the Hyperbolic Formulation of the Constraint equations for $\mathbb{T}^3$ cosmological space-times, by Alejandro Estrada-Llesta and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: gr-qc < prev | next > new | recent | 2023-09 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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