Abstract
The Plebański–Demiański class contains stationary, axially symmetric type D solutions of the Einstein–Maxwell equations with a cosmological constant. It covers many well-known black hole space-times like the Schwarzschild, Kerr or the Kottler space-time. The space-times are characterized by seven parameters: mass, spin, electric and magnetic charge, gravitomagnetic NUT charge, a so-called acceleration parameter and the cosmological constant. We review space-time properties like symmetries and isometries as well as the appearance of singularities as ring singularities or axial singularities. Furthermore, we discuss horizons, the ergoregion and a region with causality violation.
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Notes
- 1.
- 2.
Note that this parameter C has nothing to do with the name “C-metric” for space-times of accelerated black hole(s).
- 3.
Some authors call only the region between the horizon and the static limit ergoregion. This is that part of the region \(g_{tt}>0\) which an outside observer would be able to see.
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Grenzebach, A. (2016). The Plebański–Demiański Class of Black Hole Space-Times. In: The Shadow of Black Holes. SpringerBriefs in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-30066-5_2
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