Local existence theory for a class of CMC gauges for the Einstein-non-linear scalar field equations
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916954883751936 |
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| author | Ringström, Hans |
| author_facet | Ringström, Hans |
| contents | The purpose of this article is to develop a local existence theory for a class of CMC gauges for the Einstein-non-linear scalar field equations. We do so in the context of closed and parallelisable initial manifolds. The assumption that the initial manifold is parallelisable is not a topological restriction in the case of closed oriented 3-manifolds, but it is a restriction in higher dimensions. The results include local existence, uniqueness, a continuation criterion and Cauchy stability. Previous results concerning related gauges have been restricted to the case of n-torus spatial topology. Moreover, they have not covered the Einstein-non-linear scalar field setting. The main motivation for developing this theory is that it forms the basis for a family of past global non-linear stability results we derive in a separate article. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_14110 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local existence theory for a class of CMC gauges for the Einstein-non-linear scalar field equations Ringström, Hans General Relativity and Quantum Cosmology 35A01, 83C05, 83C56, 53C50, 83Cxx The purpose of this article is to develop a local existence theory for a class of CMC gauges for the Einstein-non-linear scalar field equations. We do so in the context of closed and parallelisable initial manifolds. The assumption that the initial manifold is parallelisable is not a topological restriction in the case of closed oriented 3-manifolds, but it is a restriction in higher dimensions. The results include local existence, uniqueness, a continuation criterion and Cauchy stability. Previous results concerning related gauges have been restricted to the case of n-torus spatial topology. Moreover, they have not covered the Einstein-non-linear scalar field setting. The main motivation for developing this theory is that it forms the basis for a family of past global non-linear stability results we derive in a separate article. |
| title | Local existence theory for a class of CMC gauges for the Einstein-non-linear scalar field equations |
| topic | General Relativity and Quantum Cosmology 35A01, 83C05, 83C56, 53C50, 83Cxx |
| url | https://arxiv.org/abs/2509.14110 |