Marginal tubes and foliations by marginal surfaces

Abstract In this paper, we introduce the notion of a marginal tube, which is hypersurface foliated by surfaces. It generalises marginally trapped tube and several notions black hole horizons, for example trapping isolated dynamical etc. We prove that if every spacelike section surface, then null. There no assumption on topology tube. To it, study geometry surfaces in four-dimensional spacetime with help double null coordinate systems. The result valid arbitrary spacetimes, regardless any energy condition.