# Ricci-Based Gravity theories and their impact on Maxwell and nonlinear electromagnetic models

## TL;DR

This paper explores how Ricci-Based Gravity theories relate to General Relativity when coupled with electromagnetic fields, revealing a correspondence with nonlinear electromagnetism models and discussing potential phenomenological implications.

## Contribution

It extends the correspondence between Ricci-Based Gravity theories and GR to include electromagnetic matter fields, providing a general algorithm and specific applications.

## Key findings

- Eddington-inspired Born-Infeld gravity corresponds to GR with Born-Infeld electromagnetism.
- The established algorithm relates matter fields in GR and RBG frames.
- Potential phenomenological implications of the gravity-electromagnetism correspondence.

## Abstract

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.