We study the one-loop effective action for $N$ 4D conformally invariant scalars on the spherically symmetric background. The main part of effective action is given by integration of 4D conformal anomaly. This effective action (in 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 anti-evaporation of nearly maximal SdS (Nariai) black holes takes also place in the model under consideration. Careful treatment of quantum corrections and perturbations modes of Nariai black hole is given being quite complicated. It is shown that exists also perturbation where black hole radius shrinks, i.e. black hole evaporates. We point out that our result holds for wide class of models including conformal scalars, spinors and vectors. Hence,anti-evaporation of SdS black holes is rather general effect which should be taken into account in quantum gravity considerations.
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机译：我们研究了球对称背景上$ N $ 4D保形不变标量的单环有效动作。有效行动的主要部分是通过整合4D保形异常给出的。这个有效的作用（在大的$ N $近似值和部分曲率展开中）用于研究质量最大的Schwarzschild-de Sitter（SdS）黑洞的量子演化。我们发现正在考虑的模型中也发生了几乎最大的SdS（Nariai）黑洞的抗蒸发作用（最近由Bousso和Hawking以$ N $最小标量和另一个近似有效作用发现）。给出了纳里亚黑洞的量子校正和微扰模式的仔细处理，这是相当复杂的。示出了在黑洞半径缩小，即黑洞蒸发的情况下也存在扰动。我们指出，我们的结果适用于包括共形标量，旋转子和向量在内的各种模型。因此，SdS黑洞的抗蒸发是相当普遍的效应，应在量子引力方面加以考虑。
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