Stability and antievaporation of the Schwarzschild-de Sitter black holes in bigravity

We study the stability under the perturbation and the related antievaporation of the Nariai space-time in bigravity. If we impose a specific condition for the solutions and parameters, we obtain asymptotically de Sitter space-time, and show the existence of the Nariai space-time as a background solution. Considering the perturbation around the Nariai space-time up to the first order, we investigate the behavior of the black hole horizon. We show that the antievaporation does not occur on the classical level in the bigravity.