Constant scalar curvature and warped product globally null manifolds

This paper deals with the curvature properties of a class of globally null manifolds (M,g) which admit a global null vector field and a complete Riemannian hypersurface. Using the warped product technique we study the fundamental problem of finding a warped function such that the degenerate metric g admits a constant scalar curvature on M. Our work has an interplay with the static vacuum solutions of the Einstein equations of general relativity.