On the Mathematics of Coframe Formalism and Einstein-Cartan Theory -- A Brief Review

Abstract

This article is a review of what could be considered the basic mathematics of Einstein-Cartan theory. We discuss the formalism of principal bundles, principal connections, curvature forms, gauge fields, torsion form, and Bianchi identities, and eventually, we will end up with Einstein-Cartan-Sciama-Kibble field equations and conservation laws in their implicit formulation.