  We extend the correspondence between metric-affine Ricci-Based Gravity
theories and General Relativity (GR) to the case in which the matter sector is
represented by linear and nonlinear electromagnetic fields. This complements
previous studies focused on fluids and scalar fields. We establish the general
algorithm that relates the matter fields in the GR and RBG frames and consider
some applications. In particular, we find that the so-called Eddington-inspired
Born-Infeld gravity theory coupled to Maxwell electromagnetism is in direct
correspondence with GR coupled to Born-Infeld electromagnetism. We comment on
the potential phenomenological implications of this relation.
