Título:
Stabiliy of the double-cusp spacetimes and long-time geometrizations
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Autor:
Bellati Barthés, Alejandro Gustavo
Reiris Ithurralde, Martín
Reiris Ithurralde, Martín
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Tipo de documento:
Preprint
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Palabras clave:
Differential geometry
Hyperbolic spaces
Hyperbolic spaces
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Año de publicación:
2023
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Resumen:
Since the early years of General Relativity, understanding the long-time behavior of the cosmological solutions of Einstein's vacuum equations has been a fundamental yet challenging task. Solutions with global symmetries, or perturbations thereof, have been extensively studied and are reasonably understood. On the other hand, thanks to the work of Fischer-Moncrief and M. Anderson, it is known that there is a tight relation between the future evolution of solutions and the Thurston decomposition of the spatial 3-manifold. Consequently, cosmological spacetimes developing a future asymptotic symmetry should represent only a negligible part of a much larger yet unexplored solution landscape. In this work, we revisit a program initiated by the second named author, aimed at constructing a new type of cosmological solution first posed by M. Anderson, where (at the right scale) two hyperbolic manifolds with a cusp separate from each other through a thin torus neck. Specifically, we prove that the so-called double-cusp solution, which models the torus neck, is stable under S1×S1 - symmetry-preserving perturbations. The proof, which has interest on its own, reduces to proving the stability of a geodesic segment as a wave map into the hyperbolic plane and partially relates to the work of Sideris on wave maps and the work of Ringström on the future asymptotics of Gowdy spacetimes.
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Versión permitida preprint.
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arXiv
EN:
Mathematics (Differential Geometry), arXiv: 2311.17180, nov 2023, pp. 1-30
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Citación:
Bellati Barthés, A y Reiris Ithurralde, M. "Stabiliy of the double-cusp spacetimes and long-time geometrizations". [Preprint]. Publicado en: Mathematics (Differential Geometry). arXiv: 2311.17180, nov 2023, pp 1-30 . DOI: 10.48550/arXiv.2311.17180
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Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
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| Ficheros | Descripción | Tamaño | Formato | ||
|---|---|---|---|---|---|
| 2311.17180v1.pdf | — | 720.85 KB | Adobe PDF |