On the relation between 2+1 Einstein gravity and Chern Simons theory

TL;DR

This paper investigates the relationship between 2+1 dimensional Einstein gravity and Chern-Simons theory, revealing they are not gauge equivalent and highlighting the complex effects of including singular metrics in general relativity.

Contribution

It demonstrates the non-equivalence of gauge classes in the two theories and explores the impact of singular metrics on 3D gravity.

Findings

Gauge equivalence classes differ between the theories.

Including singular metrics affects general relativity more than expected.

The theories are not physically equivalent.

Abstract

A simple example is given to show that the gauge equivalence classes of physical states in Chern Simons theory are not in one-to-one correspondence with those of Einstein gravity in three spacetime dimensions. The two theories are therefore not equivalent. It is shown that including singular metrics into general relativity has more, and in fact a quite counter-intuitive, impact on the theory than one naively expects.