A stationary vacuum solution dual to the Kerr solution

We present a stationary axially symmetric two parameter vacuum solution which could be considered as “dual ” to the Kerr solution. It is obtained by removing the mass parameter from the function of the radial coordinate and introducing a dimensionless parameter in the function of the angle coordinate in the metric functions. It turns out that it is in fact the massless limit of the Kerr- NUT solution. PACS numbers: 04.20.-q,95.30 The axially symmetric stationary spacetime hosts the most interesting two parameter Kerr family of vacuum black hole solution of the Einstein equation. It is well known that the family is unique under the assumptions of asymptotic flatness and of existence of regular smooth horizon. The Kerr solution has turned out to be the most interesting solution of the Einstein equation for the astrophysical applications, particularly in the context of high energy sources like quasars, pulsars, gamma ray bursters and active galactic nuclei. The two parameters in the solution represent mass and specific angular momentum of

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