  Spherical vacuum and scalar collapse for the Starobinsky R^2 model is
simulated. Obtained by considering the quantum-gravitational effects, this
model would admit some cases of singularity-free cosmological spacetimes. It is
found, however, that in vacuum and scalar collapse, when f' or the physical
scalar field is strong enough, a black hole including a central singularity can
be formed. In addition, near the central singularity, gravity dominates the
repulsion from the potential, so that in some circumstances the Ricci scalar is
pushed to infinity by gravity. Therefore, the semiclassical effects as included
here do not avoid the singularity problem in general relativity. A strong
physical scalar field can prevent the Ricci scalar from growing to infinity.
Vacuum collapse for the RlnR model is explored, and it is observed that for
this model the Ricci scalar can also go to infinity as the central singularity
is approached. Therefore, this feature seems universal in vacuum and scalar
collapse in f(R) gravity.
