Effective Action for Conformal Scalars and Anti-Evaporation of Black Holes

TL;DR

This paper investigates the quantum effects on Schwarzschild-de Sitter black holes using the one-loop effective action for conformally invariant scalars, revealing that anti-evaporation is a general phenomenon in such models.

Contribution

It demonstrates that anti-evaporation of nearly maximal SdS black holes occurs in models with conformal scalars, extending previous findings to a broader class of quantum fields.

Findings

Anti-evaporation effect is confirmed for conformal scalars, spinors, and vectors.

Quantum corrections can lead to black hole radius growth or shrinkage.

The results are relevant for quantum gravity models involving various quantum fields.

Abstract

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.