A Unified Approach to Solvable Models of Dilaton Gravity in Two-Dimensions Based on Symmetry

TL;DR

This paper presents a unified framework for solvable two-dimensional dilaton gravity models using non-linear sigma models with symmetry, simplifying their analysis and revealing new models with diverse cosmological terms.

Contribution

It introduces a symmetry-based formulation that unifies various dilaton gravity models and decomposes them into simpler components, including free fields and Liouville equations.

Findings

All models with vanishing cosmological constant are classified within this framework.

The space-time structure induced by matter shock waves is analyzed.

New models with and without cosmological terms are proposed.

Abstract

A large class of solvable models of dilaton gravity in two space-time dimensions, capable of describing black hole geometry, are analyzed in a unified way as non-linear sigma models possessing a special symmetry. This symmetry, which can be neatly formulated in the target-space-covariant manner, allows one to decompose the non-linearly interacting dilaton-gravity system into a free field and a field satisfying the Liouville equation with in general non-vanishing cosmological term. In this formulation, all the existent models are shown to fall into the category with vanishing cosmological constant. General analysis of the space-time structureinduced by a matter shock wave is performed and new models, with and without the cosmological term, are discussed.