A novel derivation for Kerr metric in Papapetrou gauge

We present a simple novel derivation, ab initio, of the equations appropriate for stationary axisymmetric spacetimes using the Papapetrou form of the metric (Papapetrou gauge). It is shown that using coordinates which preserve the Papapetrou gauge three separated solutions of the Ernst equations appear in the case of Kerr metric. In this context a parameter arises which represents topological defects induced by an infinite static string along the z axis. Finally, we discuss a simple solution that may be derived from the Kerr ansatz.