Loop Corrections in the Spectrum of 2D Hawking Radiation

TL;DR

This paper calculates loop corrections to the Hawking radiation spectrum in a 2D dilaton gravity model, revealing how back-reaction affects the spectrum and temperature at different loop orders.

Contribution

It provides the first detailed analysis of one-loop and two-loop back-reaction effects on Hawking radiation spectrum in the CGHS model.

Findings

Back-reaction shifts the horizon position, affecting the spectrum.

One-loop corrections do not alter the Hawking temperature.

Two-loop corrections increase the temperature threefold.

Abstract

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.