Two-loop Back-reaction in 2D Dilaton Gravity

TL;DR

This paper computes two-loop quantum corrections in 2D dilaton gravity, revealing how back-reaction affects black hole evaporation, modifies Hawking radiation, and potentially removes singularities in semi-classical geometries.

Contribution

It provides the first detailed analysis of two-loop back-reaction effects in the CGHS model, showing how higher-order corrections influence black hole evaporation and singularity resolution.

Findings

Hawking flux becomes non-thermal and vanishes at late times.

No static remnants for finite-width matter pulses, but remnants appear in shock-wave limit.

Higher-order loops can eliminate singularities in semi-classical solutions.

Abstract

We calculate the two-loop quantum corrections, including the back-reaction of the Hawking radiation, to the one-loop effective metric in a unitary gauge quantization of the CGHS model of 2d dilaton gravity. The corresponding evaporating black hole solutions are analysed, and consistent semi-classical geometries appear in the weak-coupling region of the spacetime when the width of the matter pulse is larger then the short-distance cutoff. A consistent semi-classical geometry also appears in the limit of a shock-wave matter. The Hawking radiation flux receives non-thermal corrections such that it vanishes for late times and the total radiated mass is finite. There are no static remnants for matter pulses of finite width, although a BPP type static remnant appears in the shock-wave limit. Semi-classical geometries without curvature singularities can be obtained as well. Our results indicate that higher-order loop corrections can remove the singularities encountered in the one-loop solutions.