Tests in symmetrically collapsing spacetimes and the full sub-extreme Kerr-Newman family support the conjecture that compact trapped submanifolds of codimension >1 stay inside black holes and do not reach the domain of outer communications.
Singularity theorems based on trapped submanifolds of arbitrary co-dimension
2 Pith papers cite this work. Polarity classification is still indexing.
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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.
fields
gr-qc 2years
2026 2verdicts
UNVERDICTED 2representative citing papers
Curvature conditions proposed for focal points of trapped submanifolds do not apply in general to codimensions higher than two, though they may for specific submanifolds.
citing papers explorer
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Convex foliations and trapped submanifolds
Tests in symmetrically collapsing spacetimes and the full sub-extreme Kerr-Newman family support the conjecture that compact trapped submanifolds of codimension >1 stay inside black holes and do not reach the domain of outer communications.
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Curvature conditions for generalized singularity theorems
Curvature conditions proposed for focal points of trapped submanifolds do not apply in general to codimensions higher than two, though they may for specific submanifolds.