Nonlinear Maxwell's theory mimics dark energy

Abstract

In a recent study (Sadeghi and Noori Gashti, 2024) the so-called Reissner-Nordstr & ouml;m (RN) black hole surrounded by perfect fluid dark matter (PFDM) has been investigated. Here in this Letter, we prove that technically such a black hole does not exist in the context of Maxwell's linear theory coupled minimally to a PFDM. Furthermore, it is shown that this black hole is the result of nonlinear corrections to the linear Maxwell's Lagrangian in the Einstein-Maxwell theory. The energy-momentum tensor is split into Maxwell's linear theory and a correction term. The latter i.e., the correction part of the energy-momentum tensor represents an anisotropic dark energy. This result brings the question if nonlinear electrodynamics can be the source of dark matter/energy.