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

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 gravitoelectric and gravitomagnetic charges, and a duality transformation exists 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.