Information is Not Lost in the Evaporation of 2-dimensional Black Holes

TL;DR

It is established that the future null infinity of the quantum space-time is sufficiently long for the past vacuum to evolve to a pure state in the future, and all the information comes out at future infinity; there are no remnants.

Abstract

We analyze Hawking evaporation of the Callen-Giddings-Harvey-Strominger (CGHS) black holes from a quantum geometry perspective and show that information is not lost, primarily because the quantum space-time is sufficiently larger than the classical. Using suitable approximations to extract physics from quantum space-times we establish that: i)future null infinity of the quantum space-time is sufficiently long for the the past vacuum to evolve to a pure state in the future; ii) this state has a finite norm in the future Fock space; and iii) all the information comes out at future infinity; there are no remnants.

Figures (2)

• Figure 1: A Penrose diagram of an evaporating CGHS black hole, motivated by swh1. Information can be lost in the singularity represented by the wiggly line.
• Figure 2: Proposed Penrose diagram. The mean field approximation is used in the shaded region in near ${\mathcal{I}}^{+}_{\rm R}$. Quantum fluctuations of geometry are large in the interior region around the wiggly line representing the putative classical singularity.