Exact Solutions of 1+1 Dimensional Dilaton Gravity Coupled to Matter

TL;DR

This paper derives and explicitly solves integrable models of 1+1 dimensional dilaton gravity coupled to matter, including static spherical solutions and a Hamiltonian framework for quantization.

Contribution

It introduces a class of integrable 1+1D dilaton gravity models coupled to matter and provides explicit solutions, extending to static spherical solutions and a Hamiltonian quantization approach.

Findings

Explicit solutions for integrable dilaton gravity models

Derivation of static spherical solutions in arbitrary dimensions

Outline of Hamiltonian formulation for quantization

Abstract

A class of integrable models of 1+1 dimensional dilaton gravity coupled to scalar and electromagnetic fields is obtained and explicitly solved. More general models are reduced to 0+1 dimensional Hamiltonian systems, for which two integrable classes (called s-integrable) are found and explicitly solved. As a special case, static spherical solutions of the Einstein gravity coupled to electromagnetic and scalar fields in any real space-time dimension are derived. A generalization of the `no-hair' theorem is pointed out and the Hamiltonian formulation that enables quantizing the s-integrable systems is outlined.