  It is typically believed that the additional degrees of freedom in any
modification of gravity are completely suppressed by the large energy densities
coexisting with an astrophysical black hole. In this paper, we find that this
might not always be the case. This belief holds for black holes formed via
gravitational collapse in very dense environments, whereas the black holes with
sufficiently low accretion rates that have low matter densities inside
innermost stable circular orbit will generally unscreen chameleons. We develop
a novel technique to study the dynamics of accretion of a scalar field onto a
Schwarzschild-like black hole which is accurate on both short and long time
scales. In particular, we study the behavior of the extra scalar degree of
freedom in the Starobinsky and Hu-Sawicki $f(R)$ theories, for the symmetron
model, and for the Ratra-Peebles model. Aside from calculating non-trivial
static field profiles outside the black hole, we provide the tools to study the
(in)stability and evolution towards the equilibrium solution for any generic
well behaved set of parameters and initial conditions. Our code is made
publicly available for further research and modifications to study other
models.
