Charged spherically symmetric and slowly rotating charged black hole solutions in bumblebee gravity

Abstract In this paper, we study the scenario in which the matter field is an electromagnetic field nonminimally coupled to the bumblebee vector field. We present exact charged spherically symmetric black hole solutions and slowly rotating charged solutions in bumblebee gravity with and without a cosmological constant. The static spherically symmetric solutions describe the Reissner–Nordström-like black hole and Reissner–Nordström-(anti) de Sitter-like black hole, while the stationary and axially symmetric solutions describe the Kerr–Newman-like black hole and Kerr–Newman–(anti) de Sitter-like black hole. We utilize the Hamilton–Jacobi formalism to study the shadows of the black holes. Additionally, we investigate the effect of the electric charge and Lorentz-violating parameters on the radius of the shadow reference circle and the distortion parameter. We find that the radius of the reference circle decreases with the Lorentz-violating parameter and the charge parameter, while the distortion parameter increases with the Lorentz-violating parameter and the charge parameter.