A stationary vacuum solution dual to the Kerr solution

TL;DR

This paper introduces a new stationary, axially symmetric vacuum solution in general relativity, which is a massless limit of the Kerr-NUT solution, achieved by modifying the metric functions.

Contribution

It presents a novel vacuum solution dual to Kerr by removing mass dependence and adding a dimensionless parameter, expanding the family of known exact solutions.

Findings

The solution is a massless limit of the Kerr-NUT spacetime.

It features a dual symmetry to the Kerr solution.

The metric is characterized by a new dimensionless parameter.

Abstract

We present a stationary axially symmetric two parameter vacuum solution which could be considered as ``dual'' to the Kerr solution. It is obtained by removing the mass parameter from the function of the radial coordinate and introducing a dimensionless parameter in the function of the angle coordinate in the metric functions. It turns out that it is in fact the massless limit of the Kerr - NUT solution.