The GHP formalism and a type N twisting vacuum metric with killing vector

It is shown that the formalism introduced by Geroch, Held and Penrose has a geometrical basis. With the help of the resulting insight a canonical spli tting of the complex function which appears in the standard form of the Alg ebraically Special metrics is realized. The results of this splitting are a pplied to the problem of a (special) Type N vacuum metric with a twisting p rinciple null direction. It is demonstrated that it is possible (but not fe asable) to find the metric without the use of differential equations. An es timate of the size of the metric is given.