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arXiv · 1005.1249

Singularity theorems based on trapped submanifolds of arbitrary co-dimension

Gregory J. Galloway·José M. M. Senovilla
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Abstract

Standard singularity theorems are proven in Lorentzian manifolds of arbitrary dimension n if they contain closed trapped submanifolds of arbitrary co-dimension. By using the mean curvature vector to characterize trapped submanifolds, a unification of the several possibilities for the boundary conditions in the traditional theorems and their generalization to arbitrary co-dimension is achieved. The classical convergence conditions must be replaced by a condition on sectional curvatures, or tidal forces, which reduces to the former in the cases of co-dimension 1, 2 or n.

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Gregory J. Galloway, José M. M. Senovilla. 2010-05-13. Singularity theorems based on trapped submanifolds of arbitrary co-dimension. https://doi.org/10.1088/0264-9381%2F27%2F15%2F152002

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