TL;DR
This paper presents a formulation of Einstein's gravitational equations using generalized differential forms and Cartan's equations, extending the geometric framework and exploring solutions in vacuum conditions.
Contribution
It introduces a novel approach to Einstein's equations with generalized metric connections and extends Cartan's structure equations for metric geometries.
Findings
Generalized connections can be flat in vacuum solutions.
Solutions of Einstein's equations can be related by generalized Poincaré transformations.
An action for vacuum equations is constructed using a generalized Nieh-Yan form.
Abstract
A formulation of Einstein's gravitational field equations in four space-time dimensions is presented using generalized differential forms and Cartan's equations for metric geometries. Cartan's structure equations are extended by using generalized metric connections. They are then employed to represent Einstein's field equations and their solutions. When the energy-momentum tensor is zero the generalized connections can be chosen to be flat and different solutions of Einstein's equations can be related by generalizations of the Poincar\'e group. An action for the vacuum field equations is constructed by generalizing the Nieh-Yan three-form.
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