More on the Geometric Approach for Gravitation Coupled with Electromagnetism within a Riemann-Cartan Vacuum Spacetime
Résumé
The goal of this paper is to link the geometric variables of four-dimensional spacetime with electromagnetic and gravitational fields. For that purpose, assuming a Hilbert-Einstein action with Yang-Mills action, we derive both the gravitation and the electromagnetic equation within a Riemann-Cartan spacetime where curvature and torsion are present. We thus show that the gravitational and electromagnetic fields are respectively identified as geometric objects of such a spacetime, namely the curvature for gravitation which is a classical result, and the torsion as electromagnetic fields. Moreover, the torsion tensor of the spacetime is related to the so-called flux spin angular momentum of electromagnetic waves propagating within the spacetime.
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