Static and spherically symmetric black holes in $f(R)$ theories

We study some features of static and spherically symmetric solutions (SSS) with a horizon in $f(R)$ theories of gravitation by means of a near-horizon analysis. A necessary condition for an $f(R)$ theory to have this type of solution is obtained. General features of the effective potential are deduced, and it is shown that there exists a limit on the curvature at the horizon, in both cases for any $f(R)$. Finally, we calculate the expression for the energy of the collision of two massive particles in the center of mass frame.