We prove that any metric with curvature less than or equal to $-1$ (in the sense of A. D. Alexandrov) on a closed surface of genus greater than $1$ is isometric to the induced intrinsic metric on a space-like convex surface in a Lorentzian manifold of dimension $(2+1)$ with sectional curvature $-1$ . The proof is by approximation, using a result about isometric immersion of smooth metrics by Labourie and Schlenker.

We analyze the asymptotic directional structure and properties of gravitational field of specific exact solutions belonging to the large family of black hole spacetimes of type D found by Plebański and Demiański. We discuss the structure in the case of de Sitter (Λ>0) and anti–de Sitter (Λ<0) conformal infinity. With the aim of further interpretation, we have found the relation between the structure of the sources (the mass m, the electric e and magnetic g charges, the NUT parameter l, the rotational parameter a, the acceleration α) and the properties of radiation generated by them. In particular, we studied the amplitude of radiation and illustrated it in several figures.