Canonical analysis of the BCEA topological matter model coupled to gravitation in (2+1) dimensions

TL;DR

This paper analyzes the canonical structure of a (2+1)-dimensional topological field theory derived from Chern-Simons action, exploring gauge classes and solutions relevant to Einstein gravity coupled with topological matter.

Contribution

It provides a detailed canonical analysis of a topological matter model coupled to gravity in (2+1) dimensions, including classification of gauge equivalence classes and solutions.

Findings

Identification of all gauge equivalence classes via holonomy analysis

Construction and characterization of representative solutions for each class

Insights into the topological structure of Einstein gravity with matter in (2+1)D

Abstract

We consider a topological field theory derived from the Chern - Simons action in (2+1) dimensions with the I(ISO(2,1)) group,and we investigate in detail the canonical structure of this theory.Originally developed as a topological theory of Einstein gravity minimally coupled to topological matter fields in (2+1) dimensions, it admits a BTZ black-hole solutions, and can be generalized to arbitrary dimensions.In this paper, we further study the canonical structure of the theory in (2+1) dimensions, by identifying all the distinct gauge equivalence classes of solutions as they result from holonomy considerations. The equivalence classes are discussed in detail, and examples of solutions representative of each class are constructed or identified.