Limit to general relativity in $f(R)$ theories of gravity

We discuss two aspects of $f(R)$ theories of gravity in metric formalism. We first study the reasons to introduce a scalar-tensor representation for these theories and the behavior of this representation in the limit to General Relativity, $f(R)\to R$. We find that the scalar-tensor representation is well behaved even in this limit. Then we work out the exact equations for spherically symmetric sources using the original $f(R)$ representation, solve the linearized equations, and compare our results with recent calculations of the literature. We observe that the linearized solutions are strongly affected by the cosmic evolution, which makes very unlikely that the cosmic speedup be due to $f(R)$ models with correcting terms relevant at low curvatures.