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Abstract

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 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 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 in the Schrodinger
representation and shown to be of order 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.