Loop Corrections in the Spectrum of 2D Hawking Radiation

We determine the one-loop and the two-loop back-reaction corrections in the spectrum of the Hawking radiation for the CGHS model of 2d dilaton gravity by evaluating the Bogoliubov coefficients for a massless scalar field propagating on the corresponding backgrounds. Since the back-reaction can induce a small shift in the position of the classical horizon, we find that a positive shift leads to a non-Planckian late-time spectrum, while a null or a negative shift leads to a Planckian late-time spectrum in the leading-order stationary-point approximation. In the one-loop case there are no corrections to the classical Hawking temperature, while in the two-loop case the temperature is three times greater than the classical value. We argue that these results are consistent with the behaviour of the Hawking flux obtained from the operator quantization only for the times which are not too late, in accordance with the limits of validity of the semiclassical approximation.Comment: 20 pages, latex, no figure

One-Loop Effective Action for Spherical Scalar Field Collapse

We calculate the complete one-loop effective action for a spherical scalar field collapse in the large radius approximation. This action gives the complete trace anomaly, which beside the matter loop contributions, receives a contribution from the graviton loops. Our result opens a possibility for a systematic study of the back-reaction effects for a real black hole.Comment: 14 pages, slightly expanded version to appear in Class. Quant. Gra