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October 2019 Weakly trapped submanifolds in standard static spacetimes
Allan Freitas, Henrique F. de Lima, Eraldo A. Lima Jr., Márcio S. Santos
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Ark. Mat. 57(2): 317-332 (October 2019). DOI: 10.4310/ARKIV.2019.v57.n2.a4

Abstract

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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Allan Freitas. Henrique F. de Lima. Eraldo A. Lima Jr.. Márcio S. Santos. "Weakly trapped submanifolds in standard static spacetimes." Ark. Mat. 57 (2) 317 - 332, October 2019. https://doi.org/10.4310/ARKIV.2019.v57.n2.a4

Information

Received: 26 February 2019; Revised: 28 May 2019; Published: October 2019
First available in Project Euclid: 16 April 2020

zbMATH: 1426.53079
MathSciNet: MR4018756
Digital Object Identifier: 10.4310/ARKIV.2019.v57.n2.a4

Subjects:
Primary: 53C42
Secondary: 53B30, 53C50

Rights: Copyright © 2019 Institut Mittag-Leffler

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Vol.57 • No. 2 • October 2019
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