Arkiv för Matematik
Volume 57 (2019)
Weakly trapped submanifolds in standard static spacetimes
Pages: 317 – 332
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 . Furthermore, we also investigate parabolic weakly trapped submanifolds immersed in a standard static spacetime.
standard static spacetimes, weakly trapped submanifolds, parabolic spacelike submanifolds, mean curvature vector field
2010 Mathematics Subject Classification
Primary 53C42. Secondary 53B30, 53C50.
Received 26 February 2019
Received revised 28 May 2019
Accepted 17 June 2019
Published 7 October 2019