Global Existence and Long Time Behavior in Einstein-Belinski-Zakharov Soliton Spacetimes
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866908832406437888 |
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| author | Muñoz, Claudio Trespalacios, Jessica |
| author_facet | Muñoz, Claudio Trespalacios, Jessica |
| contents | We consider the vacuum Einstein field equations under the Belinski-Zakharov symmetry, which leaves the problem as a 1+1-dimensional quasilinear system of PDEs. Depending on the chosen signature of the metric, these spacetimes contain most of the well-known special solutions in General Relativity. In this paper, {\color{blue} we consider the case of cosmological metrics, in the Belinsky-Zakharov notation}, and prove global existence of small Belinski-Zakharov spacetimes under a natural nondegeneracy condition. We also construct new energies and virial functionals to provide a description of the energy decay of smooth global cosmological metrics inside the light cone. Finally, some applications are presented in the case {\color{blue} of the particular metrics called} generalized Kasner solitons. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_01414 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Global Existence and Long Time Behavior in Einstein-Belinski-Zakharov Soliton Spacetimes Muñoz, Claudio Trespalacios, Jessica Analysis of PDEs General Relativity and Quantum Cosmology We consider the vacuum Einstein field equations under the Belinski-Zakharov symmetry, which leaves the problem as a 1+1-dimensional quasilinear system of PDEs. Depending on the chosen signature of the metric, these spacetimes contain most of the well-known special solutions in General Relativity. In this paper, {\color{blue} we consider the case of cosmological metrics, in the Belinsky-Zakharov notation}, and prove global existence of small Belinski-Zakharov spacetimes under a natural nondegeneracy condition. We also construct new energies and virial functionals to provide a description of the energy decay of smooth global cosmological metrics inside the light cone. Finally, some applications are presented in the case {\color{blue} of the particular metrics called} generalized Kasner solitons. |
| title | Global Existence and Long Time Behavior in Einstein-Belinski-Zakharov Soliton Spacetimes |
| topic | Analysis of PDEs General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2305.01414 |