Study of gravitational radiation at $\mathcal{J}$ for the general type-D Einstein-Maxwell solution with cosmological constant

We characterize the gravitational radiation present in the general Plebański-Demiański type~D solution with cosmological constant $\mathrm{\Lambda }$ of any sign. We show that radiation escapes towards infinity if and only if the acceleration parameter is non-zero. We calculate the Cotton-York tensor and the boundary stress-energy tensor at infinity for negative $\mathrm{\Lambda }$, and for positive $\mathrm{\Lambda }$ the $D$ tensor that complements initial or final data at $\mathcal{J}$. In addition, we recast a recent parametrization of this family of metrics into a new form by a simple homothety, correctly identifying $\mathrm{\Lambda }$, and study the existence and regularity of the possible axes of symmetry, searching for a relation between deficit angles and radiation.