# Enhanced Ehlers Transformation and the Majumdar-Papapetrou-NUT Spacetime

## TL;DR

This paper introduces an enhanced Ehlers transformation acting as a gravitomagnetic duality, enabling the generation of new solutions like the Kerr-Newman-NUT black hole and a non-extremal Majumdar-Papapetrou-NUT solution, with implications for black hole thermodynamics.

## Contribution

A new, more precise Ehlers transformation that incorporates electromagnetic fields and acts as a gravitomagnetic duality, expanding solution-generating techniques in general relativity.

## Key findings

- Derived the Kerr-Newman-NUT black hole using the enhanced transformation.
- Constructed a non-extremal Majumdar-Papapetrou-NUT solution.
- Analyzed the microscopic entropy via Kerr/CFT correspondence.

## Abstract

The transformation which adds (or removes) NUT charge when it is applied to electrovacuum, axisymmetric and stationary space-times is studied. After analysing the Ehlers and the Reina-Treves transformations we propose a new one, more precise in the presence of the Maxwell electromagnetic field. The enhanced Ehlers transformation proposed turns out to act as a gravitomagnetic duality, analogously to the electromagnetic duality, but for gravity: it rotates the mass charge into the gravomagnetic (or NUT) charge. As an example the Kerr-Newman-NUT black hole is obtained with the help of this enhanced transformation. Moreover a new analytical exact solution is built adding the NUT charge to a double charged black hole, at equilibrium. It describes the non-extremal generalisation of the Majumdar-Papapetrou-NUT solution. From the near-horizon analysis, its microscopic entropy, according to the Kerr/CFT correspondence, is found and the second law of black hole thermodynamics is discussed.