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**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:

[tex] \frac{du}{ds}=0 \rightarrow \nabla _{u} u=0 [/tex]

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

[tex] \nabla _{u} u=0 \rightarrow \nabla R_{ab} =0 [/tex]

Or to get Einstein equation appart from using the Lagrangian formalism... using "Differential Geomertry" or similar...