Classical and Quantum Aspects of 1+1 Gravity

TL;DR

This paper classifies all global solutions in 2D dilaton gravity, explores quantum states, and examines how the black-hole mass spectrum varies with the theory's signature, relevant for quantum gravity models.

Contribution

It provides a comprehensive classification of solutions and quantum states in 2D dilaton gravity, highlighting the impact of signature on the mass spectrum.

Findings

Maximally extended solutions include black holes and kinks.

Quantum states are explicitly determined using a Dirac approach.

Black-hole mass spectrum depends on the theory's signature.

Abstract

We present a classification of all global solutions (with Lorentzian signature) for any general 2D dilaton gravity model. For generic choices of potential-like terms in the Lagrangian one obtains maximally extended solutions on arbitrary non-compact two-manifolds, including various black-hole and kink configurations. We determine all physical quantum states in a Dirac approach. In some cases the spectrum of the (black-hole) mass operator is found to be sensitive to the signature of the theory, which may be relevant in view of current attempts to implement a generalized Wick-rotation in 4D quantum gravity.