Why not a di-NUT? or Gravitational duality and rotating solutions

TL;DR

This paper explores gravitational duality's effects on rotating solutions like Kerr-NUT black holes, proposing new definitions for dual charges and revealing their non-trivial nature in these solutions.

Contribution

It introduces a framework for understanding dual Lorentz charges in rotating spacetimes and clarifies the NUT charge's role as a dipole in Kerr solutions.

Findings

Kerr-NUT solutions possess non-trivial dual Lorentz charges.

A new approach to incorporating electric and magnetic sources in general relativity.

Kerr's source can be interpreted as a mass with a NUT charge dipole.

Abstract

We study how gravitational duality acts on rotating solutions, using the Kerr-NUT black hole as an example. After properly reconsidering how to take into account both electric (i.e. mass-like) and magnetic (i.e. NUT-like) sources in the equations of general relativity, we propose a set of definitions for the dual Lorentz charges. We then show that the Kerr-NUT solution has non-trivial such charges. Further, we clarify in which respect Kerr's source can be seen as a mass M with a dipole of NUT charges.