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Weakly trapped submanifolds in standard static spacetimes

Allan Freitas Universidade Federal da Paraíba Henrique F. de Lima Universidade Federal da Paraíba Eraldo A. Lima Universidade Federal da Paraíba Márcio S. Santos Universidade Federal da Paraíba

Differential Geometry mathscidoc:1912.43040

Arkiv for Matematik, 57, (2), 317 – 332, 2019
We study weakly trapped submanifolds of codimension two in a standard static spacetime. In this setting, we apply some generalized maximum principles in order to investigate the geometry of these trapped submanifolds. For instance, we establish sufficient conditions to guarantee that such a spacelike submanifold must be a hypersurface of the Riemannian base of the ambient spacetime. As a consequence, we prove that there do not exist n-dimensional compact (without boundary) trapped submanifolds immersed in an (n+2)-dimensional standard static spacetime. Such a nonexistence result was originally obtained for stationary spacetimes by Mars and Senovilla [20]. Furthermore, we also investigate parabolic weakly trapped submanifolds immersed in a standard static spacetime.
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@inproceedings{allan2019weakly,
  title={Weakly trapped submanifolds in standard static spacetimes},
  author={Allan Freitas, Henrique F. de Lima, Eraldo A. Lima, and Márcio S. Santos},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191204135822694711596},
  booktitle={Arkiv for Matematik},
  volume={57},
  number={2},
  pages={317 – 332},
  year={2019},
}
Allan Freitas, Henrique F. de Lima, Eraldo A. Lima, and Márcio S. Santos. Weakly trapped submanifolds in standard static spacetimes. 2019. Vol. 57. In Arkiv for Matematik. pp.317 – 332. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191204135822694711596.
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