 The case "N" > 0 (quantity "N" is time-like) leads to time singularities of interest.Substituting in "f"1 = 1/2 (ξ + "z") sin "y", "f"2 = 1/2 (ξ − "z") sin "y" results in "G" of type
This choice does not diminish the generality of conclusions; it can be shown that generality is possible (in the first approximation) just on account of the remaining permissible transformations of variables.At "N" < 0 (quantity "N" is space-like) one can substitute "G" = "z" which generalizes the well-known [[Einstein–Rosen metric]].