Black holes surrounded by massive vector fields in Kaluza-Klein gravity

We present an exact black hole solution surrounded by massive vector fields predicted by Kaluza-Klein (KK) gravity. KK gravity in four dimensions (4D) is of particular interest, as it predicts a tower of particle states, including gravitons with spin-0 and spin-1 components, in addition to the massless spin-2 gravitons of general relativity. The extra degrees of freedom in the gravitational sector modify the law of gravity, allowing the theory to explain the effects attributed to dark matter in the universe. In this paper, we construct a black hole solution surrounded by massive spin-1 gravitons within KK theory. In addition to the influence of the massive vector fields, we incorporate an interaction term between the black hole and the massive vector field. The black hole solution is affected by the mass of the spin-1 graviton and an additional parameter that encodes corrections to Newton's constant, as well as the coupling between the massive vector field and the black hole mass. We find that the coupling between the massive vector field and the black hole mimics the effect of an electric charge. To this end, we investigate the accretion disk, quasinormal modes (QNMs), and the stability of the black hole spacetime. Finally, we use Event Horizon Telescope (EHT) observations of Sgr A* to constrain the black hole parameters.