Anti-evaporation of Bardeen de-Sitter black holes

In this paper, we discuss the possibility of the anti-evaporation of degenerate Bardeen de-Sitter black hole. We solve the perturbation equations around the Nariai space–time. The solution of one of the perturbations related to the horizon size demonstrates that horizon of such black hole is constant. The other perturbation is also found to be stable. We further study thermodynamical properties of such black holes. We observe double phase transition at the Nariai limit. - Highlights: • Cosmological constant introduces a cosmological horizon in the Bardeen black hole. • Anti-evaporation is associated with the Nariai space–time. • The perturbations around degenerate horizon are stable. • The size of the degenerate horizon is constant with time. • A double phase transition occurs in the Nariai–Bardeen de-Sitter black hole.