The $D\to 2$ Limit of General Relativity

TL;DR

This paper develops a method to derive a two-dimensional theory of gravity from D-dimensional general relativity as D approaches 2, connecting it to other dimensional reduction approaches.

Contribution

It introduces a novel method for taking the D→2 limit of general relativity, resulting in a 2D theory coupled to conserved stress-energy, and relates it to existing reduction techniques.

Findings

Derived a 2D gravity theory from D-dimensional GR as D→2

Established the relationship between this limit and alternative dimensional reduction methods

Provided a framework for analyzing gravity in two dimensions

Abstract

A method for taking the $D\to 2$ limit of D-dimensional general relativity is constructed, yielding a two-dimensional theory which couples gravitation to conserved stress-energy. We show how this theory is related to those obtained via an alternative dimensional reduction approach.