Loop corrections in the spectrum of two-dimensional Hawking radiation

Abstract

We determine the one-and two-loop backreaction corrections in the spectrum of the Hawking radiation for the Callan-Giddings-Harvey-Strominger (CGHS) model of two-dimensional dilaton gravity by evaluating the Bogoliubov coefficients for a massless scalar field propagating on the corresponding backgrounds. Since the backreaction 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 times which are not too late, in accordance with the limits of validity of the semiclassical approximation.