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Paper detail

Singularity theorems based on trapped submanifolds of arbitrary co-dimension

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.

preprint2010arXivOpen access
Gregory J. GallowayJosé M. M. Senovilla
gr-qc
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Gregory J. GallowayJosé M. M. Senovilla

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