Quantum effects of the conformal anomaly in a 2D model of gravitational collapse

The macroscopic effects of the quantum conformal anomaly are evaluated in a simplified two-dimensional model of gravitational collapse. The effective action and stress tensor of the anomaly can be expressed in a local quadratic form by the introduction of a scalar conformalon field φ, which satisfies a linear wave equation. A wide class of non-vacuum initial state conditions is generated by different solutions of this equation. An interesting subclass of solutions corresponds to initial states that give rise to an arbitrarily large semi-classical stress tensor Tμν\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left\langle {T}_{\mu}^{\nu}\right\rangle $$\end{document} on the future horizon of the black hole formed in classical collapse. These lead to modification and suppression of Hawking radiation at late times after the collapse, and potentially large backreaction effects on the horizon scale due to the conformal anomaly. The probability of non-vacuum initial conditions large enough to produce these effects is estimated from the Gaussian vacuum wave functional of φ in the Schrödinger representation and shown to be O\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathcal{O} $$\end{document}(1). These results indicate that quantum effects of the conformal anomaly in non-vacuum states are relevant for gravitational collapse in the effective theory of gravity in four dimensions as well.