Theorem to generate Einstein-Non Linear Maxwell Fields

TL;DR

This paper introduces a theorem that simplifies finding solutions in Lovelock gravity coupled with non-linear electrodynamics, including black hole and radiating solutions, regardless of the order of gravity or non-linearities involved.

Contribution

It provides a general theorem linking Einstein-Lovelock equations with non-linear Maxwell fields, applicable to static, spherically symmetric, and radiating spacetimes in Lovelock gravity.

Findings

The theorem applies to pure electric fields in Lovelock gravity.

It enables construction of black hole solutions in Chern-Simons theory.

The radiating version generalizes Bonnor-Vaidya metrics in this context.

Abstract

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. $\(F_{\mu \nu}F^{\mu \nu}\)^{q},$ $q=$ finely - tuned constant) within the context of Lovelock gravity.