The classical solutions of two-dimensional gravity

TL;DR

This paper classifies solutions of two-dimensional gravity derived from a non-linear Lagrangian, analyzes their properties, and explores their relationships through conformal transformations to Einstein-dilaton gravity.

Contribution

It provides a comprehensive classification of solutions and demonstrates their equivalence via conformal transformations between different gravity models.

Findings

Solutions are classified based on symmetry and singularity properties

Conformal transformations relate solutions of different two-dimensional gravity theories

The paper establishes equivalences between non-linear Lagrangian and Einstein-dilaton gravity solutions

Abstract

The solutions of two-dimensional gravity following from a non-linear Lagrangian L = f(R) are classified, and their symmetry and singularity properties are described. Then a conformal transformation is applied to rewrite these solutions as analogous solutions of two-dimensional Einstein-dilaton gravity and vice versa.