Backreaction on Moving Mirrors and Black Hole Radiation

We compute the effect of quantum mechanical backreaction on the spectrum of radiation in a dynamical moving mirror model, mimicking the effect of a gravitational collapse geometry. Our method is based on the use of a combined WKB and saddle-point approximation to implement energy conservation in the calculation of the Bogolyubov coefficients, in which we assume that the mirror particle has finite mass m. We compute the temperature of the produced radiation as a function of time and find that after a relatively short time, the temperature is reduced by a factor 1/2 relative to the standard result. We comment on the application of this method to two-dimensional dilaton gravity with a reflecting boundary, and conclude that the WKB approximation quickly breaks down due to the appearance of naked singularities and/or white hole space-times for the relevant WKB-trajectories.