Various metric forms of all type D black holes and their application

Abstract Several recent results concerning the complete class of exact solutions to the Einstein–Maxwell–Λ equations of type D with a double-aligned electromagnetic field are summarized. This large class of spacetimes includes charged black holes with rotation, NUT parameter, and acceleration. In particular, we present their Plebański–Demiański, Griffiths–Podolský–Vrátný, and Astorino metric representations, we discuss mutual relations between them, and demonstrate their usefulness for investigation of physical and geometrical properties (singularities, horizons, conformal diagrams, ergoregions, rotating strings causing the acceleration, thermodynamics). It includes the proof that such black holes emit gravitational radiation if, and only if, they accelerate. Very recent extension to type D black holes with non-aligned Maxwell field is also mentioned.