From SR to GR in an easy math (and physical) way

From SR to GR in an "easy" math (and physical) way

Hello..i know that for example to go from Newtonian to SR you take:

$$\frac{du}{ds}=0 \rightarrow \nabla _{u} u=0$$

My question is ¿is there an "easy" form to go from SR to GR in the form:

$$\nabla _{u} u=0 \rightarrow \nabla R_{ab} =0$$
Or to get Einstein equation appart from using the Lagrangian formalism... using "Differential Geomertry" or similar...