Null Foliations of Spacetime and the Geometry of Black Hole Horizons (1908.08739v1)

Abstract: In this work, a method for constructing null foliations of spacetime is presented. This method is used to specify equivalence classes of null generators, whose representatives can be associated lightlike co-normals that are locally affine geodesic and thus locally orthogonal to embedded null hypersurfaces of spacetime. The main benefit of the proposed procedure is the fact that it is less geometrically restrictive than the traditional dual-null approaches to general relativity, but nevertheless allows for the conclusion that spacetimes can be foliated by suitable pairs of normalized null geodesic vector fields. This is demonstrated by the example of different black hole spacetimes, that is, by members of the Kerr-Newman family, according to which a said foliation and an associated equivalence class of null generators are explicitly constructed.