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

• Received 31 January 2024
• Accepted 15 April 2024

DOI:https://doi.org/10.1103/PhysRevD.109.104030