Classical and Quantum Gravity in 1+1 Dimensions, Part III: Solutions of Arbitrary Topology

TL;DR

This paper provides a comprehensive classification of all global solutions for 1+1 dimensional dilaton gravity models with arbitrary topology, revealing the structure of their solution space and topology.

Contribution

It explicitly characterizes the solution space for generic 1+1D dilaton gravity models with arbitrary topology, including smooth solutions on non-compact surfaces.

Findings

Solutions exist on any non-compact 2-surface.

Solution space is explicitly parametrized.

Topology of the reduced phase space is clarified.

Abstract

All global solutions of arbitrary topology of the most general 1+1 dimensional dilaton gravity models are obtained. We show that for a generic model there are globally smooth solutions on any non-compact 2-surface. The solution space is parametrized explicitly and the geometrical significance of continuous and discrete labels is elucidated. As a corollary we gain insight into the (in general non-trivial) topology of the reduced phase space. The classification covers basically all 2D metrics of Lorentzian signature with a (local) Killing symmetry.