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Rastall introduced a stress-energy tensor whose divergence is proportional tothe gradient of the Ricci scalar. This proposal leads to a change in the formof the field equations of General Relativity, but it preserves the number ofdegrees of freedom. Rastall's field equations can be either interpreted as GRwith a redefined SET, or it can imply different physical consequences insidethe matter sector. We investigate limits under which the Rastall fieldequations can be directly derived from an action, in particular from two$f(R)$-gravity extensions: $f(R,\mathcal L_m)$ and $f(R,T)$. We show that thereare similarities between these theories, but the Rastall SET cannot be fullyrecovered from them, apart from certain particular cases here discussed. It isremarkable that a simple, covariant and invertible redefinition of the SET, asthe one proposed by Rastall, is hard to be directly implemented in the action.

On Rastall gravity formulation as a $f(R,\mathcal{L}_m)$ and a $f(R,T)$ theory