Plebanski-Demianski goes NUTs (to remove the Misner string)

We present a general procedure, based on the Ehlers transformation of the Ernst equations, to add the gravitomagnetic mass to the whole Plebanski-Demianski family of solutions. We can efficiently generate a large class of accelerating black holes, such as Reissner-Nordstrom or Kerr-Newman, endowed with the NUT parameter. The full rotating version carries a couple of independent NUT charges, one associated to the black hole and the other to the accelerating Rindler background. The two NUT parameters can be coupled to remove the axial irregularity which causes the Misner string, still remaining with a Lorentzian spacetime, without the need to impose periodic time. All the metrics we build are not of D-type according to the Petrov classification, but type-I, so they belong to a more general category with respect to C-metrics and the Plebanski-Demianski seed. A convenient form of the most general type D black hole solution in general relativity, coupled with Maxwell electromagnetism, is obtained when switching off one of the two NUT parameters.