The weak null condition and Kaluza–Klein spacetimes
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We prove the non-linear stability of a system of non-linear wave equations satisfying the weak null condition. In particular, this includes the case of the non-linear stability of Minkowski spacetime times a [Formula: see text]-torus subject to perturbations depending only on the non-compact coordinates. Our argument closely follows the proof of the non-linear stability of Minkowski spacetime by Lindblad and Rodnianski.
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Global stability for a suitable class of initial data was proven in the case of supersymmetric compactifications in [61, 62].
“Such an analysis was undertaken in [61, 62] where stability was proven in the case of supersymmetric compactifications.”
From Gravitational memory and compact extra dimensions (2022) · cites this paper as [61]
Theorem 1.1 (Introduction, p. 1) proves nonlinear stability for zero-mode perturbations of pure Einstein theory compactified on a torus, and Theorem 2.1 (p. 7) gives conditions on small initial data under which the solution exists for all time. The paper does not establish stability for supersymmetric compactifications as such; its discussion of other compact spaces, including Calabi–Yau manifolds, presents their stability as an open question (p. 8). (LLM, conf=0.88)
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Research works printed but not linked: 3
- [3][3] Yvonne Choquet-Bruhat and Robert Geroch. Global aspects of the cauchy problem in general relativity. Comm. Math. Phys., 14(4):329–335, 1969.
- [4][4] D. Christodoulou and S. Klainerman. The Global Nonlinear Stability of the Minkowski Space, volume 41 of Princeton Mathematical Series. Princeton University Press, Princeton, NJ, 1993.
- [5][5] Demetrios Christodoulou. Global solutions of nonlinear hyperbolic equations for small initial data. Commu- nications on Pure and Applied Mathematics, 39(2):267–282, 1986.
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Gravitational memory and compact extra dimensions
Ferko, C., Satishchandran, G., & Sethi, S. (2022) · Physical Review D · doi:10.1103/physrevd.105.024072 · Cited by 20 · see citing works
- Authors
- Wyatt, Z.
- Affiliations
- Maxwell Institute for Mathematical Sciences (GB)
- Corresponding author
- Wyatt, Zoe
- ORCID
- Wyatt, Zoe
- Venue
- Journal of Hyperbolic Differential Equations
- Publisher
- World Scientific Pub Co Pte Lt
- Published
- 2018-06
- Volume
- 15
- Issue
- 02
- Pages
- 219-258
- ISSN
- 0219-8916 (ISSN-L)
- 1793-6993
- OpenAlex
- W2621026254
- Cited by
- 10
- References
- 0
- Citations by year
- 2024: 1 · 2023: 1 · 2022: 2 · 2021: 3 · 2019: 3
- FWCI
- 1.74
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Journal of Hyperbolic Differential Equations (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Edinburgh Research Explorer (University of Edinburgh) (submittedVersion, other-oa)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Mathematics › Mathematical Physics › Advanced Mathematical Physics Problems
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Engineering › Control and Systems Engineering › Stability and Controllability of Differential Equations
- Keywords
- nonlinear stability, nonlinear wave equations, Minkowski space, toroidal compactification, hyperbolic systems
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