  We study gravitational collapse for the Starobinsky $R^2$ model, a particular
example of an $f(r)$ theory, in a spherically symmetric spacetime. We add a
massless scalar field as matter content to the spacetime. We work in the
Einstein frame, where an additional scalar field arises due to the conformal
transformation. As in general relativity, depending on the initial data, we
found that the gravity scalar field and the physical scalar field can collapse,
forming a black hole, in which the final solution is the Schwarzschild metric.
We found the threshold of black hole formation through a fine-tuning method and
studied critical collapse near this regime.
