On Energy-Momentum Conservation in Non-Minimal Geometry-Matter Coupling Theories

In this work, we discuss the conditions that allow the establishment of an equivalence between f(R,T)=R+λh(T) gravity models and General Relativity (GR) coupled to a modified matter sector. We do so by considering a D-dimensional spacetime and the matter sector described by nonlinear electrodynamics and/or a scalar field. We find that, for this particular family of models, the action and field equations can indeed be written in terms of a modified matter source within GR. However, when several matter sources are combined, this interpretation is no longer possible if h(T) is a nonlinear function, due to the emergence of crossed terms that mix together the scalar and vector sectors.