298 research outputs found
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.Comment: 11 pages, no figures, some corrections
Boost invariant marginally trapped surfaces in Minkowski 4-space
The extremal and partly marginally trapped surfaces in Minkowski 4-space,
which are invariant under the group of boost isometries, are classified.
Moreover, it is shown that there do not exist extremal surfaces of this kind
with constant Gaussian curvature. A procedure is given in order to construct a
partly marginally trapped surface by gluing two marginally trapped surfaces
which are invariant under the group of boost isometries. As an application, a
proper star-surface is constructed.Comment: 13 pages, comment added in section
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