Hawking radiation from dilaton gravity in 1 + 1 dimensions: a pedagogical review

TL;DR

This paper reviews the complex issue of Hawking radiation in 2D dilaton gravity, presenting a new solution that simplifies flux calculations and discusses ongoing debates about conformal frames and theoretical approaches.

Contribution

It introduces a minimal-input solution to Hawking flux in spherically reduced gravity, resolving negative flux contributions and providing a closed-form integrated action.

Findings

Exact cancellation of negative flux contributions

Asymptotic agreement with minimally coupled scalar results

Critical discussion of conformal frame issues

Abstract

Hawking radiation in d=4 is regarded as a well understood quantum theoretical feature of Black Holes or of other geometric backgrounds with an event horizon. On the other hand, the dilaton theory emerging after spherical reduction and generalized dilaton theories only during the last years became the subject of numerous studies which unveiled a surprisingly difficult situation. Recently we have found some solution to the problem of Hawking flux in spherically reduced gravity which has the merit of using a minimal input. It leads to exact cancellation of negative contributions to this radiative flux, encountered in other approaches at infinity, so that our result asymptotically coincides with the one of minimally coupled scalars. The use of an integrated action is avoided - although we have been able to present also that quantity in a closed expression. This short review also summarizes and critically discusses recent activities in this field, including the problem of ``conformal frames'' for the background and questions which seem to be open in our own approach as well as in others.