A Unitary S-matrix for 2D Black Hole Formation and Evaporation

TL;DR

This paper constructs a unitary quantum S-matrix for a 2D dilaton gravity model with scalar fields, demonstrating black hole formation and evaporation, and draws parallels with the c=1 matrix model.

Contribution

It introduces a well-defined 2D toy model with a unitary S-matrix that captures black hole dynamics and connects it to matrix model results.

Findings

The S-matrix is explicitly constructed and shown to be unitary.

The model describes black hole formation and Hawking evaporation.

A correspondence with the c=1 matrix model is established.

Abstract

We study the black hole information paradox in the context of a two-dimensional toy model given by dilaton gravity coupled to $N$ massless scalar fields. After making the model well-defined by imposing reflecting boundary conditions at a critical value of the dilaton field, we quantize the theory and derive the quantum quantum $S$-matrix for the case that $N$=$24$. This $S$-matrix is unitary by construction, and we further argue that in the semiclassical regime it describes the formation and subsequent Hawking evaporation of two-dimensional black holes. Finally, we note an interesting correspondence between the dilaton gravity $S$-matrix and that of the $c=1$ matrix model.