A novel derivation for Kerr metric in Papapetrou gauge

TL;DR

This paper introduces a new derivation of the Kerr metric equations within the Papapetrou gauge, revealing solutions with topological defects and discussing a related simple solution.

Contribution

It provides a novel, straightforward derivation of Kerr metric equations in Papapetrou gauge, highlighting solutions with topological defects and a related simple solution.

Findings

Three separated solutions of the Ernst equations in Kerr metric

Existence of topological defects from an infinite static string

Discussion of a simple solution derived from the Kerr ansatz

Abstract

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.