Contact structures on null hypersurfaces

The aim of this paper is to show how we can induce contact structures, metric structures and Sasaki on a null hypersurface from rigging vector field. We give several explicit examples construction some obstructions its existence. For example, be introduced only zero mean curvature hypersurfaces, whereas in totally geodesic ones. In particular construct Kähler halo around an isolated horizon black hole. also study the stability construction. prove that close enough (resp. Sasaki) connected by one parameter family structures.