  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.
