Anti-Evaporation of Schwarzschild-de Sitter Black Holes in $F(R)$
  gravity
  We studied the anti-evaporation of degenerate Schwarzschild-de Sitter black
hole (so-called Nariai space-time) in modified $F(R)$ gravity. The analysis of
perturbations of the Nariai black hole is done with the conclusion that
anti-evaporation may occur in such a theory already on classical level. For
several power-law $F(R)$ gravities which may describe the inflation and/or dark
energy eras we presented the theory parameters bounds for occurrence of
anti-evaporation and conjectured creation of infinite number of horizons.
