%0 Journal Article %T Anti-Evaporation of Schwarzschild-de Sitter Black Holes in $F(R)$ gravity %A Shin'ichi Nojiri %A Sergei D. Odintsov %J Physics %D 2013 %I arXiv %R 10.1088/0264-9381/30/12/125003 %X 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. %U http://arxiv.org/abs/1301.2775v3