The galaxy rotation curves in the $f(R,T)$ modified gravity formalism

Astronomical data have shown that the galaxy rotation curves are mostly flat in the far distance of the galactic cores, which reveals the insufficiency of our knowledges about how gravity works in these regimes. In this paper we introduce a resolution of this issue from the $f(R,T)$ modified gravity formalism perspective. By investigating two classes of models with separable (minimal coupling model) and inseparable (non-minimal coupling model) parts of the Ricci scalar $R$ and trace of the energy-momentum tensor $T$, we find that only in the latter models it is possible to attain flat galaxy rotation curves.