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

Abstract

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