Integrable 1+1 dimensional gravity models

TL;DR

This paper reviews integrable 1+1 and 0+1 dimensional dilaton gravity models, discussing their solutions, Hamiltonian formulation, quantization, and applications, including a generalized 'no-hair' theorem.

Contribution

It provides a comprehensive review of integrable dilaton gravity models, introduces new results, and simplifies existing formulations, expanding understanding of their solutions and applications.

Findings

Models are solvable via explicit quadratures or Liouville equation.

0+1 models emerge as sectors of non-integrable 1+1 models.

A generalized 'no-hair' theorem is proven.

Abstract

Integrable models of dilaton gravity coupled to electromagnetic and scalar matter fields in dimensions 1+1 and 0+1 are briefly reviewed. The 1+1 dimensional integrable models are either solved in terms of explicit quadratures or reduced to the classically integrable Liouville equation. The 0+1 dimensional integrable models emerge as sectors in generally non integrable 1+1 dimensional models and can be solved in terms of explicit quadratures. The Hamiltonian formulation and the problem of quantizing are briefly discussed. Applications to gravity in any space - time dimension are outlined and a generalization of the so called `no - hair' theorem is proven using local properties of the Lagrange equations for a rather general 1+1 dimensional dilaton gravity coupled to matter. This report is based on the paper hep-th/9605008 but some simplifications, corrections and new results are added.