  The transformation which adds (or removes) NUT charge when it is applied to
electrovacuum, axisymmetric and stationary space-times is studied. After
analysing the Ehlers and the Reina-Treves transformations we propose a new one,
more precise in the presence of the Maxwell electromagnetic field. The enhanced
Ehlers transformation proposed turns out to act as a gravitomagnetic duality,
analogously to the electromagnetic duality, but for gravity: it rotates the
mass charge into the gravomagnetic (or NUT) charge. As an example the
Kerr-Newman-NUT black hole is obtained with the help of this enhanced
transformation. Moreover a new analytical exact solution is built adding the
NUT charge to a double charged black hole, at equilibrium. It describes the
non-extremal generalisation of the Majumdar-Papapetrou-NUT solution. From the
near-horizon analysis, its microscopic entropy, according to the Kerr/CFT
correspondence, is found and the second law of black hole thermodynamics is
discussed.
