Black Holes and Nonperturbative Canonical 2D Dilaton Gravity

TL;DR

This paper presents a nonperturbative canonical quantization of 2D dilaton gravity, demonstrating that black holes in this framework do not violate unitarity or cause information loss, with implications for real black hole quantum behavior.

Contribution

It introduces a novel canonical transformation approach based on Bäcklund transformations, enabling a unitary quantization of dilaton gravity and black hole evaporation.

Findings

Black holes in this model do not violate unitarity.

Information escapes during black hole evaporation.

The quantization scheme has implications for real black hole quantum mechanics.

Abstract

We investigate nonperturbative canonical quantization of two dimensional dilaton gravity theories with an emphasis on the CGHS model. We use an approach where a canonical transformation is constructed such that the constraints take a quadratic form. The required canonical transformation is obtained by using a method based on the B\"acklund transformation from the Liouville theory. We quantize dilaton gravity in terms of the new variables, where it takes a form of a bosonic string theory with background charges. Unitarity is then established by going into a light-cone gauge. As a direct consequence, black holes in this theory do not violate unitarity, and there is no information loss. We argue that the information escapes during the evaporation process. We also discuss the implications of this quantization scheme for the quantum fate of real black holes. The main conclusion is that black holes do not have to violate quantum mechanics.