Theorem to generate Einstein–nonlinear Maxwell fields

We present a theorem in d-dimensional static, spherically symmetric spacetime in generic Lovelock gravity coupled with a non-linear electrodynamic source to generate solutions. The theorem states that irrespective of the order of the Lovelock gravity and non-linear 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 (CS) theory is given. Radiating version of the theorem has been considered, which generalizes the Bonnor-Vaidya (BV) metric to the Lovelock gravity with a NLM field as a radiating source. We consider also the radiating power - Maxwell source (i. e. \\ (F\ \F^\ \\\) ^q, q= finely - tuned constant) within the context of Lovelock gravity.