Comment on "Reissner-Nordstr\"{o}m Black Holes in the Inverse Electrodynamics Model, [arXiv:1407.4383]"

TL;DR

This paper comments on the inverse electrodynamics model (IEM), showing it belongs to a broader class of nonlinear electrodynamics with zero trace energy-momentum tensor, and discusses its implications for dyonic Reissner-Nordström black holes.

Contribution

It demonstrates that the IEM model is part of a more general class of nonlinear electrodynamics characterized by a traceless energy-momentum tensor.

Findings

IEM belongs to a broader class of nonlinear electrodynamics.

Dyonic Reissner-Nordström black hole solutions are part of this general class.

The model's solutions have specific properties related to the energy-momentum tensor trace.

Abstract

Recently, the inverse electrodynamics model (IEM) was introduced and applied to fined Reissner-Nordstr\"{o}m black holes in the context of the general relativity coupled minimally with the nonlinear electrodynamics \cite{1}. The solution consists of both electric and magnetic fields as of the dyonic solutions. Here in this note, we show that the IEM model belongs to a more general class of nonlinear electrodynamics with $T=T_{\mu }^{\mu }=0$. Here $T_{\mu }^{\nu }$ is the energy-momentum tensor of the nonlinear electrodynamic Lagrangian. Naturally, such a dyonic RN black hole solution is the solution for this general class.