Genericity of singularities in spacetimes with weakly trapped submanifolds
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910884585013248 |
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| author | Silva, Ivan Pontual Costa e Espinoza, Victor Luis |
| author_facet | Silva, Ivan Pontual Costa e Espinoza, Victor Luis |
| contents | Using the standard Whitney topologies on spaces of Lorentzian metrics, we show that the existence of causal incomplete geodesics is a $C^\infty$-generic feature within the class of spacetimes of a given dimension $n\geq 3$ that are stably causal, satisfy the timelike convergence condition (``strong energy condition'') and contain a codimension-two spacelike weakly trapped closed submanifold such as, e.g., a marginally outer trapped surface (MOTS). By using a singularity theorem of Galloway and Senovilla for spacetimes containing trapped closed submanifolds of codimension higher than two we also prove an analogous $C^\infty$-genericity result for stably causal spacetimes with a suitably modified curvature condition and weakly trapped closed spacelike submanifold of any codimension $k> 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_03421 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Genericity of singularities in spacetimes with weakly trapped submanifolds Silva, Ivan Pontual Costa e Espinoza, Victor Luis Differential Geometry General Relativity and Quantum Cosmology Using the standard Whitney topologies on spaces of Lorentzian metrics, we show that the existence of causal incomplete geodesics is a $C^\infty$-generic feature within the class of spacetimes of a given dimension $n\geq 3$ that are stably causal, satisfy the timelike convergence condition (``strong energy condition'') and contain a codimension-two spacelike weakly trapped closed submanifold such as, e.g., a marginally outer trapped surface (MOTS). By using a singularity theorem of Galloway and Senovilla for spacetimes containing trapped closed submanifolds of codimension higher than two we also prove an analogous $C^\infty$-genericity result for stably causal spacetimes with a suitably modified curvature condition and weakly trapped closed spacelike submanifold of any codimension $k> 2$. |
| title | Genericity of singularities in spacetimes with weakly trapped submanifolds |
| topic | Differential Geometry General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2309.03421 |