Electrostatic and magnetostatic solutions in a Lorentz-violating electrodynamics model

We propose an effective Lorentz-violating electrodynamics model via the static de Sitter metric, which is deviated from the Minkowski metric by a minuscule amount depending on the cosmological constant. We obtain the electromagnetic field equations via the vierbein decomposition of the tensors. In addition, as an application of the electromagnetic field equations obtained, we derive the solutions of the electrostatic field and the magnetostatic field due to a point charge and a circle current, respectively, and discuss the implication of the effect of Lorentz violation in our electromagnetic theory.