Geometrodynamical Formulation of Two-Dimensional Dilaton Gravity and the Quantum Birkhoff Theorem

TL;DR

This paper develops a geometrodynamical formulation for 2D dilaton gravity, enabling a unified quantum treatment that aligns with classical Birkhoff theorem results, thus advancing the understanding of quantum black holes in lower dimensions.

Contribution

It introduces a new geometrodynamical framework for 2D dilaton gravity that facilitates its quantization and reproduces classical Birkhoff theorem outcomes at the quantum level.

Findings

Unified quantum description of 2D dilaton gravity.

Quantization aligns with classical Birkhoff theorem.

Generalized geometrodynamical variables for the model.

Abstract

General two-dimensional pure dilaton-gravity can be discussed in a unitary way by introducing suitable field redefinitions. The new fields are directly related to the original spacetime geometry and in the canonical picture they generalize the well-known geometrodynamical variables used in the discussion of the vacuum dilatonic black hole. So the model can be quantized using the techniques developed for the latter case. The resulting quantum theory coincides with the quantum theory obtained imposing the Birkhoff theorem at the classical level.