Conformal Vector Fields and Null Hypersurfaces - Atindogbé, Cyriaque; Olea, Benjamín (Springer, 2022)
We give conditions for a conformal vector field to be tangent to a null hypersurface. We particularize to two important cases: a Killing vector field and a closed and conformal vector field. In the first case, we obtain a result ensuring that a null hypersurface is a Killing horizon. In the second one, the vector field gives rise to a foliation of the manifold by totally umbilical hypersurfaces with constant mean curvature which can be spacelike, timelike or null. We prove several results which ensure that a null hypersurface with constant null mean curvature is a leaf of this foliation.
Keywords: Algebra de vectores; Null hypersurface; Rigging technique; Conformal vector field; Maximum principle; Killing horizon