Complete Classification of 1+1 Gravity Solutions

TL;DR

This paper provides a comprehensive classification of all maximally extended solutions in 1+1 gravity models, including generalized dilaton gravity and models with torsion, across various topologies.

Contribution

It offers the first complete classification of 1+1 gravity solutions with arbitrary topology and explicitly parametrizes their moduli space.

Findings

Solutions exist on non-compact surfaces of any genus with holes.

The moduli space of solutions is explicitly parametrized.

No restrictions on the topology of solutions.

Abstract

A classification of the maximally extended solutions for 1+1 gravity models (comprising e.g. generalized dilaton gravity as well as models with non-trivial torsion) is presented. No restrictions are placed on the topology of the arising solutions, and indeed it is found that for generic models solutions on non-compact surfaces of arbitrary genus with an arbitrary non-zero number of holes can be obtained. The moduli space of classical solutions (solutions of the field equations with fixed topology modulo gauge transformations) is parametrized explicitly.