  We consider the effect of the \emph{Varying Speed of Light} theory on
non-rotating black holes. We show that in any varying-$c$ theory, the
Schwarzschild solution is neither static nor stationary. For a no-charged black
hole, the singularity in the Schwarzschild horizon cannot be removed by
coordinate transformation. Hence, no matter can enter the horizon, and the
interior part of the black hole is separated from the rest of the Universe. If
$\dot{c}<0$, then the size of the Schwarzschild radius increases with time. The
higher value of the speed of light in the very early Universe may have caused a
large reduction in the probability of the creation of the primordial black
holes and their population.The same analogy is also considered for the charged
black holes.
