Lorentzian metrics from characteristic surfaces

The following issue is raised and discussed; when do families of foliations by hypersurfaces on a given four-dimensional manifold without further structure become the null surfaces of some unknown, but to be determined, metric gab(x). Explicit conditions for these surfaces are found, so that they do define a unique conformal metric with the surfaces themselves being characteristics of that metric. By giving an additional function (to be the conformal factor), full knowledge of the metric is determined. It is clear from these results that one can use these surfaces (and the conformal factor) as fundamental variables for describing any Lorentzian geometry and in particular for its use in general relativity.