Plebanśki-Demiański à la Ehlers-Harrison: Exact Rotating and Accelerating Type I Black Holes

Abstract

Recently, it was shown that type D black holes, encompassed in the large Plebanśki--Demiański (PD) family, exhibit a wide class of algebraically general generalizations via the application of Ehlers and Harrison transformations. In this work, we first discuss some mathematical details behind the composition of such transformations, and next, we introduce a qualitative picture of the most general type I generalization of the PD family, dubbed ``Enhanced Plebanśki--Demiański'' spacetime. We provide the exact form of the solution in the original PD coordinates, obtained via the simultaneous action of an Ehlers and a Harrison transformation on the vacuum PD geometry. In order to make the physics more transparent, we explicitly construct a rotating and accelerating black hole which further has NUT parameter and electric charges, both of them entering, not only the event horizon, but the Rindler horizon as well. This solution is directly obtained in the ``physical'' coordinates recently proposed by Podolský and Vrátny. Finally, a pedagogical appendix is thoughtfully included, providing readers with a user-friendly step-by-step guide to the Ernst formalism, in an attempt to address and resolve various minor inconsistencies frequently appearing in the relevant literature.

V3 matches published version in Gen Relativ Gravit (accepted on September 16)

References in corpus (9)

• Thermodynamics of Regular Accelerating Black Holes
• Accelerating Taub-NUT and Eguchi-Hanson solitons in four dimensions
• Ehlers transformations as a tool for constructing accelerating NUT black holes
• New form of all black holes of type D with a cosmological constant
• Exploring Accelerating Hairy Black Holes in $2+1$ Dimensions: The Asymptotically Locally Anti-de Sitter Class and its Holography
• Plebanski-Demianski goes NUTs (to remove the Misner string)
• Accelerating and Charged Type I Black Holes
• Thermodynamics of accelerating AdS${}_4$ black holes from the covariant phase space
• Equivalence principle and generalised accelerating black holes from binary systems

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• Generation of gravitating solutions with Baryonic charge from Einstein-Scalar-Maxwell seeds
• Nonperfect Carrollian Fluids Through Holography