Theorem to generate Einstein-nonlinear Maxwell fields

We present a theorem in a d-dimensional static, spherically symmetric spacetime in generic Lovelock gravity coupled with a nonlinear electrodynamic source to generate solutions. The theorem states that irrespective of the order of the Lovelock gravity and nonlinear Maxwell (NLM) Lagrangian, for the pure electric field case the NLM equations are satisfied by virtue of the Einstein-Lovelock equations. Applications of the theorem, specifically to the study of black hole solutions in Chern-Simons theory is given. A radiating version of the theorem has been considered, which generalizes the Bonnor-Vaidya metric to the Lovelock gravity with a NLM field as a radiating source. We consider also the radiating power-Maxwell source (i.e. (F mu nu F mu nu)(q), q = finely tuned constant) within the context of Lovelock gravity.