Induced Riemannian structures on null hypersurfaces

Abstract

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

26 pages

References in corpus (1)

• Global decomposition of a Lorentzian manifold as a Generalized Robertson-Walker space

Cited by in corpus (4)

• Surface gravity of compact non-degenerate horizons under the dominant energy condition
• Optimal transport on null hypersurfaces and the null energy condition
• Null hypersurfaces in Lorentzian manifolds with the null energy condition
• Horizon classification via Riemannian flows