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The global stability of the Kaluza–Klein spacetime
Open accessAbstract
In this paper, we show the classical global stability of the flat Kaluza–Klein spacetime, which corresponds to Minkowski spacetime in \mathbb{R}^{1+4} with one direction compactified on a circle. We consider small perturbations which are allowed to vary in all directions including the compact direction. These perturbations lead to the creation of massless modes and Klein–Gordon modes. On the analytic side, this leads to a PDE system coupling wave equations to an infinite sequence of Klein–Gordon equations with different masses. The techniques we use are based purely in physical space using the vector field method. In addition to Kaluza–Klein stability, our techniques can be easily adapted to provide a new proof of the stability of the Minkowski solution to the Einstein–Klein–Gordon equations.
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Cited by
Hou, F., Tao, F., & Yin, H. (2025) · Journal of the London Mathematical Society · doi:10.1112/jlms.70303 · Cited by 2
Metadata
- Authors
- Huneau, C., Stingo, A., & Wyatt, Z.
- Affiliations
- École Polytechnique (FR)
- University of Cambridge (GB)
- Venue
- Journal of the European Mathematical Society
- Published
- 2025-07-18
- ISSN
- 1435-9855 (ISSN-L)
- 1435-9863
- OpenAlex
- W4412871944
- Semantic Scholar
- 89393283b3324e32820ea9b61f0d70ce23bb26df
- Cited by
- 1
- References
- 0
- Citations by year
- 2025: 1
- FWCI
- 0.69
- Type
- journal article
- Language
- en
- Open access
- diamond
- doi.org
- Licence
- cc-by
- Locations
- Journal of the European Mathematical Society (publishedVersion, cc-by)
- HAL (submittedVersion, other-oa)
- Topics
- Physical Sciences › Mathematics › Mathematical Physics › Advanced Mathematical Physics Problems
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Physical Sciences › Mathematics › Applied Mathematics › Geometric Analysis and Curvature Flows
- Keywords
- global stability, Minkowski space, massless modes, Einstein-Klein-Gordon equations, vector field method, wave equation, small perturbations, physical space
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
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Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
