Abstract
AbstractGiven a null hypersurface in a Lorentzian manifold we can construct a Riemannian metric on it called the rigged metric. This is not a canonical construction because it depends on the choice of a rigging, that is, a vector field transverse to the null hypersurface, but it can be used as an auxiliary tool which allows us to apply Riemannian techniques on null hypersurfaces. We show two such applications: in the first one the rigged metric is used to obtain conditions for a totally umbilic null hypersurface to be contained in a null cone. In the second one it is used to ensure that a codimension two spacelike submanifold through a null hypersurface is a leaf of the (integrable) screen distribution.KeywordsNull hypersurfaceRigging techniqueRigged metricNull coneCodimension two spacelike submanifoldMaximum principle
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