Solution to 2+1 Gravity in DreiBein formalism

TL;DR

This paper explicitly reduces 2+1 gravity in the dreibein formalism to holonomies, demonstrating their relation to geometry and how to generate them from initial data.

Contribution

It provides a detailed method to relate dreibein formalism to holonomies and generate holonomies from initial data in 2+1 gravity.

Findings

Explicit reduction of dreibein formalism to holonomies

Method to relate holonomies to classical geometry

Procedure to generate holonomies from initial data

Abstract

The reduction of the dreibein formalism of 2+1 General Relativity to the holonomies is explicitly performed. We also show explicitly how to relate these holonomies to a geometry classically, and how to generate these holonomies from any initial data for 2+1 gravity obeying the constraints.