On complete trapped submanifolds in globally hyperbolic spacetimes
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866916117531852800 |
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| author | Albujer, Alma L. Herrera, Jónatan Rubio, Rafael M. |
| author_facet | Albujer, Alma L. Herrera, Jónatan Rubio, Rafael M. |
| contents | The aim of this manuscript is to obtain rigidity and non-existence results for parabolic spacelike submanifolds with causal mean curvature vector field in orthogonally splitted spacetimes, and in particular, in globally hyperbolic spacetimes. We also obtain results regarding the geometry of submanifolds by ensuring, under some mild hypothesis, the non-existence of local minima or maxima of certain distinguished function. Furthermore, in this last case the submanifold does not need to be parabolic or even complete.
As an application in General Relativity, we obtain several nice results regarding (non-necessarily closed) trapped surfaces in a huge family of spacetimes. In fact, we show how our technique allows us to recover some relevant previous results for trapped surfaces in both, standard static spacetimes and Generalized Robertson-Walker spacetimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_04458 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On complete trapped submanifolds in globally hyperbolic spacetimes Albujer, Alma L. Herrera, Jónatan Rubio, Rafael M. Differential Geometry Mathematical Physics The aim of this manuscript is to obtain rigidity and non-existence results for parabolic spacelike submanifolds with causal mean curvature vector field in orthogonally splitted spacetimes, and in particular, in globally hyperbolic spacetimes. We also obtain results regarding the geometry of submanifolds by ensuring, under some mild hypothesis, the non-existence of local minima or maxima of certain distinguished function. Furthermore, in this last case the submanifold does not need to be parabolic or even complete. As an application in General Relativity, we obtain several nice results regarding (non-necessarily closed) trapped surfaces in a huge family of spacetimes. In fact, we show how our technique allows us to recover some relevant previous results for trapped surfaces in both, standard static spacetimes and Generalized Robertson-Walker spacetimes. |
| title | On complete trapped submanifolds in globally hyperbolic spacetimes |
| topic | Differential Geometry Mathematical Physics |
| url | https://arxiv.org/abs/2402.04458 |