Abstract
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.
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Acknowledgments
This article is based on the results of the bachelor thesis [22] by G.B. We thank Adriano Viganò for interesting discussions on the subject, Jiří Podolský and anonymous JHEP referee for useful comments. M.A. would like to thank the Universidad Austral de Chile (UACh) and the Centro de Estudios Cientificos (CECs) for the hospitality while part of this work was done. A Mathematica notebook containing the main solutions presented in this article can be found in the arXiv source folder.
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Astorino, M., Boldi, G. Plebanski-Demianski goes NUTs (to remove the Misner string). J. High Energ. Phys. 2023, 85 (2023). https://doi.org/10.1007/JHEP08(2023)085
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DOI: https://doi.org/10.1007/JHEP08(2023)085