Black holes of type D revisited: relating their various metric forms

Abstract

We investigate a complete family of spacetimes which represent black holes with rotation, NUT twist, acceleration, electric and magnetic charges. These are exact solutions of the Einstein-Maxwell equations with any cosmological constant, such that the (non-null) electromagnetic field is aligned with both the double-degenerate principal null directions of the Weyl tensor. In particular, we explicitly relate various coordinates and the corresponding physical parameters of such solutions, namely the original Plebanski-Demianski (PD) form, the convenient Astorino (A) form which was found recently, and formally improved here (A+), the Griffiths-Podolsky (GP), and Podolsky-Vratny (PV) form of the metric. It is demonstrated that, if properly mapped and physically interpreted, all these representations cover the complete class of type D black holes. Using the new A-parameters, the two main PD quartic metric functions are factorized into the product of quadratic expressions, enabling thus an explicit analysis. Moreover, we clarify the role of the twist parameter $\omega$, related to both the Kerr-like rotation and the NUT parameters $a$ and $l$, respectively. Special attention is payed to the elusive subclass of accelerating NUT black holes with $a=0$.

51 pages, 1 figure, 1 table. Final version accepted for publication in Phys. Rev. D (with updated references and corrected typos)

References in corpus (8)

• Accelerating Kerr-Newman black holes in (anti-)de Sitter space-time
• Accelerating Taub-NUT and Eguchi-Hanson solitons in four dimensions
• New form of all black holes of type D with a cosmological constant
• Plebanski-Demianski goes NUTs (to remove the Misner string)
• Accelerating and Charged Type I Black Holes
• Equivalence principle and generalised accelerating black holes from binary systems
• Most general Type-D Black Hole and the Accelerating Reissner-Nordstrom-NUT-(A)dS solution
• Is the type-D NUT C-metric really "missing" from the most general Plebański-Demiański solution?

Cited by in corpus (7)

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• New class of rotating charged black holes with nonaligned electromagnetic field
• Kerr-Newman black hole in a Melvin-swirling universe
• Revisiting black holes of algebraic type D with a cosmological constant
• Conserved quantities and integrability for massless spinning particles in general relativity
• Conical singularity in spacetimes with NUT is observer-dependent
• Various metric forms of all type D black holes and their application