Observer-dependent Gauss–Codazzi formalism for null hypersurfaces in the space–time

We introduce a new Gauss–Codazzi framework for null hypersurfaces in the space–time. First, with the use of space–time splitting techniques, and working within the framework of general coordinates of the ambient space–time, we generalize the second fundamental form and the Ricci and Gauss–Codazzi formulae of a non-null hypersurface Σ to a neighbourhood of it. Then in a similar way we introduce a second fundamental form analogue for the null hypersurface case, and deduce the corresponding Ricci and Gauss–Codazzi formulae.