Conditions on a NULL (cas 101051-09-6) hypersurface of a Lorentzian manifold to be a NULL (cas 101051-09-6) cone

Add time:08/18/2019    Source:sciencedirect.com

We prove that a totally umbilic NULL (cas 101051-09-6) hypersurface whose Ricci curvature vanishes on null tangent vectors is contained in a null cone. For this, we use the rigging technique to induce a Riemannian metric on the null hypersurface, which is locally decomposed as a warped product with a one-dimensional base. This allows us to prove that all null geodesics in the null hypersurface pass through a common point.

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