Solutions of arbitrary topology in 1+1 gravity

TL;DR

This paper classifies all global solutions in 2D dilaton gravity models, revealing that generic potentials allow maximally extended solutions on all non-compact two-surfaces, unlike some specific models with restricted topologies.

Contribution

It provides a comprehensive classification of solutions in 2D dilaton gravity, including arbitrary topologies, extending previous results limited to specific models.

Findings

Generic potentials admit maximally extended solutions on all non-compact surfaces.

Certain popular models restrict possible spacetime topologies.

The classification encompasses all global solutions for these models.

Abstract

We present a classification of all global solutions for generalized 2D dilaton gravity models (with Lorentzian signature). While for some of the popular choices of potential-like terms in the Lagrangian, describing, e.g., string inspired dilaton gravity or spherically reduced gravity, the possible topologies of the resulting spacetimes are restricted severely, we find that for generic choices of these `potentials' there exist maximally extended solutions to the field equations on all non-compact two-surfaces.