Dark photon - dark energy stationary axisymmetric black holes

Using Ernst formalism, stationary axisymmetric black hole solution in Einstein-dark matter-dark energy gravity has been elaborated. The dark sector was chosen as dark photon concept, where an auxiliary U(1)-gauge field coupled to ordinary Maxwell one was introduced, while dark energy was modelled by the existence of positive cosmological constant. Refining our studies to the case of vanishing cosmological constant, the uniqueness theorem for the black hole in question has been proved.