Nonlinear Maxwell’s theory mimics dark energy

Abstract

In a recent study (Sadeghi and Noori Gashti, 2024) the so-called Reissner–Nordström (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.