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In this document, I analyze two new consequences of the GTR2 proposal. The main purpose is to connect that approach with usual concepts in physics. First, I prove the existence of a formal link with Yang-Mills electromagnetic fields. Second, I reconsider the notion of time, especially the conditions allowing a unique chronology. At the end, I prove that a link with Lorentz transformations can be realized for a spherically symmetric and diagonal Friedmann Robertson Walker metric.