A novel derivation for Kerr metric in Papapetrou gauge

We present a novel simple derivation, ab initio, of the equations appropriate for stationary axisymmetric space-times which enables a simple and immediate integration of the metric functions using the Papapetrou form of the metric (Papapetrou gauge). In this context it will be shown for the Kerr metric that using ``physical'' coordinates, i.e. coordinates related to the cylindrical ones from a relation which does not involve the parameters that caracterize the source, three separated solutions of the Ernst equations appear. These are geometrically different and not related one to the others by a continuous variation of the parameters of the source. It is suggested that this more physical handling of the Kerr metric is in agreement with the cosmic censorship conjecture. In this context a new parameter arises representing topological defects induced from a infinite static string along the z axis. Finally we discuss a simple solution that may be derived from the Kerr ansatz