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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2201.08347 |
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| _version_ | 1866918406758858752 |
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| author | Avalos, Rodrigo Lira, Jorge Marque, Nicolas |
| author_facet | Avalos, Rodrigo Lira, Jorge Marque, Nicolas |
| contents | In this paper, we study the coupled Einstein constraint equations on complete manifolds through the conformal method, focusing on non-compact manifolds with flexible asymptotics. This is physically well-motivated by standard cosmological space-times with non-compact Cauchy hypersurfaces, which favour general bounded geometry manifolds rather than a specific model for infinity. First, we prove an existence criterion on complete manifolds with appropriate barrier functions for physically well-motivated coupled systems. Then, in the bounded geometry case, we build barrier functions and thus show existence. We also prove an existence result on compact manifolds with boundary for a wider family of coupled systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_08347 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Einstein Type Systems on Complete Manifolds Avalos, Rodrigo Lira, Jorge Marque, Nicolas Analysis of PDEs Mathematical Physics 35J60, 58J05, 83C05 In this paper, we study the coupled Einstein constraint equations on complete manifolds through the conformal method, focusing on non-compact manifolds with flexible asymptotics. This is physically well-motivated by standard cosmological space-times with non-compact Cauchy hypersurfaces, which favour general bounded geometry manifolds rather than a specific model for infinity. First, we prove an existence criterion on complete manifolds with appropriate barrier functions for physically well-motivated coupled systems. Then, in the bounded geometry case, we build barrier functions and thus show existence. We also prove an existence result on compact manifolds with boundary for a wider family of coupled systems. |
| title | Einstein Type Systems on Complete Manifolds |
| topic | Analysis of PDEs Mathematical Physics 35J60, 58J05, 83C05 |
| url | https://arxiv.org/abs/2201.08347 |