Gravitational field of a rotating gravitational dyon

TL;DR

This paper derives a comprehensive solution to Einstein's equations describing the gravitational field of a rotating dyon with both mass and NUT charge, revealing a duality symmetry and connection to Kerr-NUT solutions.

Contribution

It presents the most general axially symmetric stationary solution with separable equations, unifying rotating dyons and Kerr-NUT metrics.

Findings

Solution describes gravitational field of a rotating dyon with dual charges.

Duality relation links charges and coordinates, preserving invariance.

Solution reduces to Kerr-NUT form, confirming its uniqueness.

Abstract

We have obtained the most general solution of the Einstein vacuum equation for the axially symmetric stationary metric in which both the Hamilton-Jacobi equation for particle motion and the Klein - Gordon equation are separable. It can be interpreted to describe the gravitational field of a rotating dyon, a particle endowed with both gravoelectric (mass) and gravomagnetic (NUT parameter) charge. Further, there also exists a duality relation between the two charges and the radial and the polar angle coordinates which keeps the solution invariant. The solution can however be transformed into the known Kerr - NUT solution indicating its uniqueness under the separability of equations of motion.