Canonical Structure of 2D Black Holes

TL;DR

This paper analyzes the canonical structure of 2D black hole solutions in dilaton gravity, revealing that the conjugate variable to black hole mass relates to differences in local time translations at infinities, generalizing Birkhoff's theorem.

Contribution

It identifies the canonical variables for 2D black holes and generalizes Birkhoff's theorem within this context.

Findings

The conjugate variable to black hole mass is the difference in local time translations at infinities.

The canonical structure depends on the choice of the Cauchy surface.

The work extends Birkhoff's theorem to 2D dilaton gravity.

Abstract

We determine the canonical structure of two-dimensional black-hole solutions arising in $2D$ dilaton gravity. By choosing the Cauchy surface appropriately we find that the canonically conjugate variable to the black hole mass is given by the difference of local (Schwarzschild) time translations at right and left spatial infinities. This can be regarded as a generalization of Birkhoff's theorem.