  The semiclassical effects of antievaporating black holes can be discussed in
the framework of $f(R)$ gravity. In particular, the
Bousso-Hawking-Nojiri-Odinstov antievaporation instability of degenerate
Schwarzschild-de Sitter black holes (the so called Nariai space-time) leads to
a dynamical increasing of black hole horizon in $f(R)$ gravity. This phenomenon
causes the following transition: emitting marginally trapped surfaces become
space-like surfaces before the effective Bekenstein-Hawking emission time. As a
consequence, Bousso-Hawking thermal radiation cannot be emitted in an
antievaporating Nariai black hole. Possible implications in cosmology and black
hole physics are also discussed.
