Effective action for conformal scalars and antievaporation of black holes

We study the one-loop effective action for N 4D conformally invariant scalers on the spherically symmetric background. The main part of the effective action is given by integration of the 4D conformal anomaly. This effective action tin large N approximation and partial curvature expansion) is applied to investigate the quantum evolution of Schwarzschild-de Sitter (SdS) black holes of maximal mass. We find that the effect (recently discovered by Bousso and Hawking for N minimal scalars and another approximate effective action) of antievaporation of nearly maximal SdS (Nariai) black holes also occurs in the model under consideration. Careful treatment of quantum corrections and perturbations modes of Nariai black holes is given, being quite complicated. It is shown that exists also perturbation where the black hole radius shrinks, i.e. the black hole evaporates. We point out that our result holds for a wide class of model, including conformal scalars, spinors and vectors. Hence, antievaporation of SdS black holes is a rather general effect which should be taken into account in quantum gravity considerations.