On scalar curvature in lightlike geometry

We introduce the concept of induced scalar curvature of a class C[M]C[M] of lightlike hypersurfaces (M,g,S(TM)), of a Lorentzian manifold, such that MM admits a canonical screen distribution S(TM), a canonical lightlike transversal vector bundle and an induced symmetric Ricci tensor. We prove that there exists such a class C[M]C[M] of a globally hyperbolic warped product spacetime [J.K. Beem, P.E. Ehrlich, K.L. Easley, Global Lorentzian Geometry, 2nd edition, Marcel Dekker, Inc. New York, 1996, MR1384756 (97f:53100)] of general relativity. In particular, we calculate the scalar curvature of a member of C[M]C[M] in a globally hyperbolic spacetime of constant curvature, supported by an example.