Can electromagnetic charge inhabit in Rastall gravity?

Abstract

One of the eminent generalizations of theory of general relativity is the Rastall gravity which was {constructed} based on the assumption of the non-conserved energy-momentum tensor of the matter field. Despite in the literature several solutions of black holes in the Rastall gravity coupled to the electromagnetic field have been presented, in the current paper we argue that the Rastall gravity with non-conserved energy-momentum tensor (with $\lambda\neq0$ and $R\neq0$) cannot couple to the electrodynamics, i.e., the electromagnetically charged black hole solution cannot be obtained in this case. This statement is adequate for both linear and nonlinear electrodynamics with the electric, magnetic, or dyonic charges coupled to the Rastall gravity.