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arXiv · 1207.1030

Induced Riemannian structures on null hypersurfaces

Manuel Gutierrez·Benjamin Olea
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Abstract

Given a null hypersurface $L$ of a Lorentzian manifold, we construct a Riemannian metric $\widetilde{g}$ on it from a fixed transverse vector field $ζ$. We study the relationship between the ambient Lorentzian manifold, the Riemannian manifold $(L,\widetilde{g})$ and the vector field $ζ$. As an application, we prove some new results on null hypersurfaces, as well as known ones, using Riemannian techniques.

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Manuel Gutierrez, Benjamin Olea. 2017-07-25. Induced Riemannian structures on null hypersurfaces. https://doi.org/10.1002/mana.201400355

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