Foliations of lightlike hypersurfaces and their physical interpretation

This paper deals with a family of lightlike (null) hypersurfaces (H _u ) of a Lorentzian manifold M such that each null normal vector ℓ of H _u is not entirely in H _u , but, is defined in some open subset of M around H _u . Although the family (H _u ) is not unique, we show, subject to some reasonable condition(s), that the involved induced objects are independent of the choice of (H _u ) once evaluated at u = constant. We use (n+1)-splitting Lorentzian manifold to obtain a normalization of ℓ and a well-defined projector onto H, needed for Gauss, Weingarten, Gauss-Codazzi equations and calculate induced metrics on proper totally umbilical and totally geodesic H _u . Finally, we establish a link between the geometry and physics of lightlike hypersurfaces and a variety of black hole horizons.