The most general axially symmetric electrovac spacetime adimitting separable equations of motion

TL;DR

This paper derives the most general axially symmetric electrovac spacetime solution allowing separable equations of motion, revealing duality invariance and encompassing rotating gravitational dyons with both electric and magnetic charges.

Contribution

It presents the comprehensive solution for axially symmetric electrovac spacetimes with separable equations, unifying various known solutions and highlighting duality symmetry.

Findings

Solution exhibits invariance under mass-NUT and radial-angle duality transformations.

Encompasses rotating gravitational dyons with electric and magnetic charges.

Can be extended to radiating solutions asymptotic to Vaidya spacetime.

Abstract

We obtain the most general solution of the Einstein electro - vacuum equation for the stationary axially symmetric spacetime in which the Hamilton-Jacobi and Klein - Gordon equations are separable. The most remarkable feature of the solution is its invariance under the duality transformation involving mass and NUT parameter, and the radial and angle coordinates. It is the general solution for a rotating (gravitational dyon) particle which is endowed with both gravoelectric and gravomagnetic charges, and there exists a duality transformation from one to the other. It also happens to be a transform of the Kerr - NUT solution. Like the Kerr family, it is also possible to make this solution radiating which asymptotically conforms to the Vaidya null radiation.