Scalarized dyonic black holes in vector-tensor Horndeski gravity

The vector-tensor Horndeski theory is supplemented by a real, massless scalar field nonminimally coupled to the Horndeski interaction term. The generic dyonic Reissner-Nordstrom solutions characterized by electric and magnetic charges, acquire an instability and bifurcate into electromagnetically charged solutions presenting a horizon and a cloud of scalar hairs at specific values of the nonminimal coupling constant. These hairy black holes are studied in terms of the physical parameters of the model and the critical phenomena limiting their domain of existence are discussed.