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.

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Cited by in corpus (9)

• Testing Generalized Einstein-Cartan-Kibble-Sciama Gravity using Weak Deflection Angle and Shadow Cast
• Covariant phase space for gravity with boundaries: metric vs tetrad formulations
• Fundamental Theory of Torsion Gravity
• Gravity with torsion as deformed $BF$ theory
• Gravitational Constraints on a Lightlike boundary
• Boundary structure of the standard model coupled to gravity
• On the Role of Einstein-Cartan Gravity in Fundamental Particle Physics
• Pati-Salam model in curved space-time from square root Lorentz manifold
• Phase space for gravity with boundaries