The Two-Dimensional Analogue of General Relativity

TL;DR

This paper explores the two-dimensional analogue of General Relativity, showing it emerges as a limit of the two-dimensional Brans-Dicke theory, similar to higher dimensions, despite the incompatibility of standard General Relativity in two dimensions.

Contribution

It identifies the two-dimensional analogue of General Relativity as a limit of two-dimensional Brans-Dicke theory, extending the understanding of gravitational theories in lower dimensions.

Findings

Two-dimensional General Relativity is not viable.

The two-dimensional analogue arises from the limit of Brans-Dicke theory.

This analogue parallels the higher-dimensional case.

Abstract

General Relativity in three or more dimensions can be obtained by taking the limit $\omega\rightarrow\infty$ in the Brans-Dicke theory. In two dimensions General Relativity is an unacceptable theory. We show that the two-dimensional closest analogue of General Relativity is a theory that also arises in the limit $\omega\rightarrow\infty$ of the two-dimensional Brans-Dicke theory.