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.