Effective action for conformal scalars and antievaporation of black holes

We study the one-loop effective action for N 4D conformally invariant scale rs 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 applie d to investigate the quantum evolution of Schwarzschild-de Sitter (SdS) bla ck holes of maximal mass. We find that the effect (recently discovered by B ousso and Hawking for N minimal scalars and another approximate effective a ction) of antievaporation of nearly maximal SdS (Nariai) black holes also o ccurs in the model under consideration. Careful treatment of quantum correc tions and perturbations modes of Nariai black holes is given, being quite c omplicated. It is shown that exists also perturbation where the black hole radius shrinks, i.e. the black hole evaporates. We point out that our resul t holds for a wide class of model, including conformal scalars, spinors and vectors. Hence, antievaporation of SdS black holes is a rather general eff ect which should be taken into account in quantum gravity considerations.