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A note on magnetic generalizations of the Kerr and Kerr–Newman solutions

A concise form of the asymptotically flat metrics describing the simplest magnetic generalizations of the Kerr and Kerr–Newman spacetimes is presented. The explicit formulae for the corresponding electromagnetic potentials are also given, together with simple expressions of all metric functions in the equatorial plane. It is shown that the magnetic field changes the structure of the gravitational multipole moments of the vacuum Kerr solution.