An extension of Birkhoff's theorem to a class of 2-d gravity theories containing black holes

TL;DR

This paper extends Birkhoff's theorem to a broad class of 2-dimensional gravity models, including dilaton gravity and spherically symmetric reductions, providing new analytic solutions and insights into their properties.

Contribution

It generalizes Birkhoff's theorem to various 2D gravity theories and derives explicit analytic solutions under a new gauge choice.

Findings

Birkhoff's theorem applies to all considered models.

Analytic solutions are obtained in the conformal gauge.

Discussion of scalar field coupling and quantization issues.

Abstract

A class of 2-dimensional models including 2-d dilaton gravity, spherically symmetric reduction of d-dimensional Einstein gravity and other related theories are classically analyzed. The general analytic solutions in the absence of matter fields other than a U(1) gauge field are obtained under a new gauge choice and recast in the conventional conformal gauge. These solutions imply that Birkhoff's theorem, originally applied to spherically symmetric 4-d Einstein gravity, can be applied to all models we consider. Some issues related to the coupling of massless scalar fields and the quantization are briefly discussed.