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Plebanski-Demianski goes NUTs (to remove the Misner string). (arXiv:2305.03744v4 [gr-qc] UPDATED)

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We present a general procedure, based on the Ehlers transformation of the
Ernst equations, to add the gravomagnetic 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.

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