Quantum evolution of Schwarzschild–de Sitter (Nariai) black holes

We calculate the one-loop effective action for conformal matter (scalars, spinors, and vectors) on spherically symmetric background. Such an effective action (in the large N approximation and expansion on curvature) is used to study quantum aspects of Schwarzschild–de Sitter (SdS) black holes (BHs) in the nearly degenerated limit (Nariai BH). We show that for all types of the above matter SdS BHs may evaporate or antievaporate in accordance with a recent observation by Bousso and Hawking for minimal scalars. Some remarks about the energy flow for SdS BHs in the regime of evaporation or antievaporation are also made. The study of the no boundary condition shows that this condition supports antievaporation for nucleated BHs (at least in the frame of our approximation). That indicates the possibility that some pair created cosmological BHs may not only evaporate but also antievaporate. Hence cosmological primordial BHs may survive much longer than expected.