Utilize este identificador para referenciar este registo:
http://hdl.handle.net/10071/31402
Autoria: | Costa, J. L. Duarte, R. Mena, F. C. |
Data: | 2023 |
Título próprio: | Improved decay estimates and C2-asymptotic stability of solutions to the Einstein-scalar field system in spherical symmetry |
Título da revista: | Journal of Hyperbolic Differential Equations |
Volume: | 20 |
Número: | 4 |
Paginação: | 853 - 902 |
Referência bibliográfica: | Costa, J. L., Duarte, R., & Mena, F. C. (2023). Improved decay estimates and C2-asymptotic stability of solutions to the Einstein-scalar field system in spherical symmetry. Journal of Hyperbolic Differential Equations, 20(4), 853-902. https://doi.org/10.1142/S021989162350025X |
ISSN: | 0219-8916 |
DOI (Digital Object Identifier): | 10.1142/S021989162350025X |
Palavras-chave: | Einstein equations Global existence of solutions Asymptotic analysis |
Resumo: | We investigate the asymptotic stability of solutions to the characteristic initial value problem for the Einstein (massless) scalar field system with a positive cosmological constant. We prescribe spherically symmetric initial data on a future null cone with a wider range of decaying profiles than previously considered. New estimates are then derived in order to prove that, for small data, the system has a unique global classical solution. We also show that the solution decays exponentially in (Bondi) time and that the radial decay is essentially polynomial, although containing logarithmic factors in some special cases. This improved asymptotic analysis allows us to show that, under appropriate and natural decaying conditions on the initial data, the future asymptotic solution is differentiable, up to and including spatial null-infinity, and approaches the de Sitter solution, uniformly, in a neighborhood of infinity. Moreover, we analyze the decay of derivatives of the solution up to second order showing the (uniform) C2-asymptotic stability of the de Sitter attractor in this setting. This corresponds to a surprisingly strong realization of the cosmic no-hair conjecture. |
Arbitragem científica: | yes |
Acesso: | Acesso Embargado |
Aparece nas coleções: | BRU-RI - Artigos em revistas científicas internacionais com arbitragem científica |
Ficheiros deste registo:
Ficheiro | Tamanho | Formato | |
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article_102926.pdf | 817,25 kB | Adobe PDF | Ver/Abrir |
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