  Due to the failure of Birkhoff's theorem, black holes in f(R) gravity
theories in which an effective time-varying cosmological "constant" is present
are, in general, dynamical. Clifton's exact spherical solution of R^(1+\delta)
gravity, which is dynamical and describes a central object embedded in a
spatially flat universe, is studied. It is shown that apparent black hole
horizons disappear and a naked singularity emerges at late times.
